Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1050 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 184 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. #21462311 | C2 | semidirect |
| 2. #21461951 | C2 | semidirect |
| 3. #21461814 | C2 | semidirect |
| 4. #21461741 | C2 | semidirect |
| 5. #21461537 | C2 | semidirect |
| 18. #16840139 | C4 | semidirect |
| 19. #16840138 | C4 | semidirect |
| 20. #16840137 | C4 | semidirect |
| 22. C61×#493 | C4 | semidirect |
| 36. C2×D488 | C2×C4 | semidirect |
| 37. C2×#11758199 | C2×C4 | semidirect |
| 40. #14519774 | C2×C4 | semidirect |
| 42. #14519773 | C2×C4 | semidirect |
| 44. C4×#92418 | C2×C4 | semidirect |
| 45. C8×Dic61 | C2×C4 | semidirect |
| 46. C2×D8×C61 | C2×C4 | semidirect |
| 47. #127×C61 | C2×C4 | semidirect |
| 48. C4×C8×C61 | C2×C4 | semidirect |
| 141. #493 | #6923 | semidirect |
| 151. C61 | #22276 | semidirect |
| 158. C2×D8 | C2×#6923 | semidirect |
| 164. #127 | C2×#6923 | semidirect |
| 175. C4×C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462311 | 2 |
| #21461951 | 2 |
| #21461814 | 2 |
| #21461741 | 2 |
| #21461537 | 2 |
| #493×D61 | 2 |
| #22276 | 61 |