Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 23. #16839509 | C4 | semidirect |
| 24. #16839508 | C4 | semidirect |
| 25. #16839507 | C4 | semidirect |
| 26. C61×#332 | C4 | semidirect |
| 212. #332 | #6923 | semidirect |
| 213. C61 | #9562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461998 | 2 |
| #21461946 | 2 |
| #21461931 | 2 |
| #21461612 | 2 |
| #21460698 | 2 |
| #21460648 | 2 |
| #332×D61 | 2 |
| #9562 | 61 |