Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
582 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 2. #21461555 | C2 | semidirect |
| 4. #21460661 | C2 | semidirect |
| 12. #16840608 | C4 | semidirect |
| 13. #16840605 | C4 | semidirect |
| 18. C2×#14519706 | C4 | semidirect |
| 19. C2×C22⋊#92418 | C4 | semidirect |
| 21. C2×C8×Dic61 | C4 | semidirect |
| 22. C23×C8×C61 | C4 | semidirect |
| 103. C23×C61 | #97 | semidirect |
| 128. C2×Dic61 | #97 | semidirect |
| 136. C8×C61 | #99 | semidirect |
| 176. C23×C8 | #6923 | semidirect |
| 192. C61 | #8160 | semidirect |
| 278. C23 | #14519831 | semidirect |
| 308. C8 | #14519835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519835 | 2 |
| #21461555 | 2 |
| #21461054 | 2 |
| #21460661 | 2 |
| C2×C8×C22⋊D61 | 2 |
| #8160 | 61 |