Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21461953 | C2 | semidirect |
| 2. #21461952 | C2 | semidirect |
| 3. #21461532 | C2 | semidirect |
| 4. #21461377 | C2 | semidirect |
| 5. #21461166 | C2 | semidirect |
| 6. #21461165 | C2 | semidirect |
| 20. #16840165 | C4 | semidirect |
| 21. #16840138 | C4 | semidirect |
| 22. #16840109 | C4 | semidirect |
| 26. C61×#486 | C4 | semidirect |
| 92. C4×#6923 | D8 | semidirect |
| 188. #486 | #6923 | semidirect |
| 202. C61 | #9847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461953 | 2 |
| #21461952 | 2 |
| #21461532 | 2 |
| #21461377 | 2 |
| #21461166 | 2 |
| #21461165 | 2 |
| #21456397 | 2 |
| #9847 | 61 |