Sigma_1 (A,C,r,q): ((0, 2, 3, 1), (1, 0, 3, 2), (0, 1, 3, 2), (2, 3, 0, 1))
Sigma_2 (B,C,q,r): ((0, 2, 3, 1), (1, 0, 3, 2), (0, 1, 3, 2), (2, 3, 0, 1))
Delta classes: sizes [8, 4, 4, 4, 2, 2, 2, 1] |N/U| [8, 2, 4, 2, 2, 2, 2, 1]
S4 classes: sizes [24, 12, 12, 8, 6, 6, 6, 4, 3, 2, 1] |N/U| [24, 2, 4, 2, 2, 6, 2, 1, 1, 2, 1]
restrictions via Sigma_1: [(3, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 2, 0, 0, 0, 0), (1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 3, 0, 0), (0, 0, 0, 1, 0, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1)]
restrictions via Sigma_2: [(3, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0, 0), (0, 2, 1, 0, 0, 0, 0, 0), (1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 3, 0, 0, 0), (0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 1), (0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1)]
h_n = |Hom(L,S_n)|: [1, 1, 1, 1, 1, 1, 1441, 30241, 282241, 1572481, 13608001, 100457281, 1494218881]
a_n(L) (number of subgroups of index n), n = 1..40:
  a_1 = 1
  a_2 = 0
  a_3 = 0
  a_4 = 0
  a_5 = 0
  a_6 = 12
  a_7 = 28
  a_8 = 16
  a_9 = 0
  a_10 = 20
  a_11 = 0
  a_12 = 0
  a_13 = 52
  a_14 = 56
  a_15 = 120
  a_16 = 0
  a_17 = 0
  a_18 = 264
  a_19 = 0
  a_20 = 120
  a_21 = 672
  a_22 = 176
  a_23 = 0
  a_24 = 448
  a_25 = 400
  a_26 = 624
  a_27 = 432
  a_28 = 2912
  a_29 = 464
  a_30 = 480
  a_31 = 1984
  a_32 = 2048
  a_33 = 2112
  a_34 = 4352
  a_35 = 3360
  a_36 = 14688
  a_37 = 4736
  a_38 = 7600
  a_39 = 14976
  a_40 = 7680
brute force |Hom(L,S_1)| = 1 ; formula 1 ; OK
brute force |Hom(L,S_2)| = 1 ; formula 1 ; OK
brute force |Hom(L,S_3)| = 1 ; formula 1 ; OK
brute force |Hom(L,S_4)| = 1 ; formula 1 ; OK
brute force |Hom(L,S_5)| = 1 ; formula 1 ; OK
brute force |Hom(L,S_6)| = 1441 ; formula 1441 ; OK
brute force |Hom(L,S_7)| = 30241 ; formula 30241 ; OK
