Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #21462175 | C2 | semidirect |
| 4. #108×#6923 | C2 | semidirect |
| 5. #21460898 | C2 | semidirect |
| 6. #21460862 | C2 | semidirect |
| 23. #16839578 | C4 | semidirect |
| 24. #16839576 | C4 | semidirect |
| 25. #16839574 | C4 | semidirect |
| 26. C61×#362 | C4 | semidirect |
| 174. #362 | #6923 | semidirect |
| 180. C61 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462175 | 2 |
| #21462135 | 2 |
| #21461970 | 2 |
| #108×#6923 | 2 |
| #21460898 | 2 |
| #21460862 | 2 |
| #21447567 | 2 |
| #13137 | 61 |