Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. M32×#6923 | C2 | semidirect |
| 4. #108×#6923 | C2 | semidirect |
| 5. #21460895 | C2 | semidirect |
| 6. #21460894 | C2 | semidirect |
| 19. #16840680 | C4 | semidirect |
| 26. #16839576 | C4 | semidirect |
| 27. #16839575 | C4 | semidirect |
| 28. #16839574 | C4 | semidirect |
| 29. C61×#361 | C4 | semidirect |
| 40. #14519852 | C2×C4 | semidirect |
| 44. #14519847 | C2×C4 | semidirect |
| 64. #14519717 | C2×C4 | semidirect |
| 67. #14519713 | C2×C4 | semidirect |
| 70. M32×C61 | C2×C4 | semidirect |
| 71. #108×C61 | C2×C4 | semidirect |
| 176. #6923 | #361 | direct (N × H) |
| 213. #361 | #6923 | direct (N × H) |
| 217. C61 | C4×#361 | semidirect |
| 242. M32 | C2×#6923 | semidirect |
| 249. #108 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#6923 | 2 |
| D61⋊#361 | 2 |
| M32×#6923 | 2 |
| #108×#6923 | 2 |
| #21460895 | 2 |
| #21460894 | 2 |
| #361×D61 | 2 |
| C4×#361 | 61 |