Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462310 | C2 | semidirect |
| 3. #21461329 | C2 | semidirect |
| 5. #21460673 | C2 | semidirect |
| 6. #21460642 | C2 | semidirect |
| 22. #16840165 | C4 | semidirect |
| 23. #16840110 | C4 | semidirect |
| 24. #16840109 | C4 | semidirect |
| 28. C61×#500 | C4 | semidirect |
| 214. #500 | #6923 | semidirect |
| 231. C61 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462310 | 2 |
| #21461955 | 2 |
| #21461329 | 2 |
| #21461250 | 2 |
| #21460673 | 2 |
| #21460642 | 2 |
| #21456941 | 2 |
| #9300 | 61 |