Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21444456 | C2 | semidirect |
| 4. #21444369 | C2 | semidirect |
| 6. #21443691 | C2 | semidirect |
| 7. C61×#1288 | C2 | semidirect |
| 10. #16840167 | C4 | semidirect |
| 11. #16840135 | C4 | semidirect |
| 12. #16840113 | C4 | semidirect |
| 13. #16840109 | C4 | semidirect |
| 161. #1288 | D61 | semidirect |
| 186. C61 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456537 | 2 |
| #21454889 | 2 |
| #21444456 | 2 |
| #21444369 | 2 |
| #21444365 | 2 |
| #21443691 | 2 |
| C61×#1288 | 2 |
| #9415 | 61 |