Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1148 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 224 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. #21462665 | C2 | semidirect |
| 2. #21461307 | C2 | semidirect |
| 3. #21461280 | C2 | semidirect |
| 4. #21461273 | C2 | semidirect |
| 8. #16840783 | C22 | semidirect |
| 9. C4×#11758217 | C22 | semidirect |
| 10. #16840618 | C22 | semidirect |
| 11. #16840618 | C22 | semidirect |
| 12. #16840617 | C22 | semidirect |
| 13. #16840617 | C22 | semidirect |
| 166. C61 | #17688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462665 | 2 |
| #21461307 | 2 |
| #21461280 | 2 |
| #21461273 | 2 |
| #21459613 | 2 |
| #17688 | 61 |