Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21448536 | C2 | semidirect |
| 4. #21444492 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 11. #16840167 | C4 | semidirect |
| 12. #16840109 | C4 | semidirect |
| 187. #1286 | D61 | semidirect |
| 214. C61 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456942 | 2 |
| #21448536 | 2 |
| #21446650 | 2 |
| #21444492 | 2 |
| #21444378 | 2 |
| #21443647 | 2 |
| C61×#1286 | 2 |
| #9300 | 61 |