Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462155 | C2 | semidirect |
| 4. #21461739 | C2 | semidirect |
| 5. #21460899 | C2 | semidirect |
| 6. #21460878 | C2 | semidirect |
| 22. #16839885 | C4 | semidirect |
| 23. #16839884 | C4 | semidirect |
| 24. #16839883 | C4 | semidirect |
| 30. C61×#444 | C4 | semidirect |
| 203. #444 | #6923 | semidirect |
| 219. C61 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462155 | 2 |
| #21462146 | 2 |
| #21462126 | 2 |
| #21461739 | 2 |
| #21460899 | 2 |
| #21460878 | 2 |
| #21454733 | 2 |
| #12829 | 61 |