Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
12446 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 6264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×#6923 | C2 | direct (N × H) |
| 7. C2×Q8×#6923 | C22 | direct (N × H) |
| 10. C23×Dic122 | C4 | semidirect |
| 11. C22×Q8×D61 | C4 | semidirect |
| 14. C23×Q8×C61 | C4 | semidirect |
| 16. C23×#6923 | Q8 | direct (N × H) |
| 19. Q8×#6923 | C23 | direct (N × H) |
| 23. C22×Dic122 | C2×C4 | semidirect |
| 24. C2×Q8×D61 | C2×C4 | semidirect |
| 29. C22×Q8×C61 | C2×C4 | semidirect |
| 37. C22×#6923 | C2×Q8 | direct (N × H) |
| 40. C2×Q8×C61 | C22×C4 | semidirect |
| 43. Q8×D61 | C22×C4 | semidirect |
| 47. C2×Dic122 | C22×C4 | semidirect |
| 50. C23×C61 | C4×Q8 | semidirect |
| 52. C22×D61 | C4×Q8 | semidirect |
| 58. C2×#6923 | C22×Q8 | direct (N × H) |
| 61. Q8×C61 | C23×C4 | semidirect |
| 66. Dic122 | C23×C4 | semidirect |
| 68. C22×C61 | C2×C4×Q8 | semidirect |
| 70. C2×D61 | C2×C4×Q8 | semidirect |
| 76. #6923 | C23×Q8 | direct (N × H) |
| 83. C2×C61 | C22×C4×Q8 | semidirect |
| 85. D61 | C22×C4×Q8 | semidirect |
| 91. C23×Q8 | #6923 | direct (N × H) |
| 98. C61 | C23×C4×Q8 | semidirect |
| 103. C22×Q8 | C2×#6923 | direct (N × H) |
| 123. C2×Q8 | C22×#6923 | direct (N × H) |
| 139. C23 | Q8×#6923 | direct (N × H) |
| 142. Q8 | C23×#6923 | direct (N × H) |
| 156. C22 | C2×Q8×#6923 | direct (N × H) |
| 165. C2 | C22×Q8×#6923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×#6923 | 2 |
| C23×C4⋊#6923 | 2 |
| C23×C4×#6923 | 2 |
| C23×Q8×D61 | 2 |
| C23×C4×Q8 | 61 |