Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21454916 | C2 | semidirect |
| 3. #21444332 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 7. C61×#1287 | C2 | semidirect |
| 10. #16840142 | C4 | semidirect |
| 11. #16840135 | C4 | semidirect |
| 12. #16840113 | C4 | semidirect |
| 13. #16840109 | C4 | semidirect |
| 168. #1287 | D61 | semidirect |
| 196. C61 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456777 | 2 |
| #21454916 | 2 |
| #21444332 | 2 |
| #21444328 | 2 |
| #21444287 | 2 |
| #21443647 | 2 |
| C61×#1287 | 2 |
| #9282 | 61 |