Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
884 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 190 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. #21462599 | C2 | semidirect |
| 2. #21461978 | C2 | semidirect |
| 3. #21461821 | C2 | semidirect |
| 4. #21461621 | C2 | semidirect |
| 17. #16840147 | C4 | semidirect |
| 18. #16840139 | C4 | semidirect |
| 19. #16840136 | C4 | semidirect |
| 21. C61×#494 | C4 | semidirect |
| 26. #14519848 | D4 | semidirect |
| 27. #14519847 | D4 | semidirect |
| 134. #494 | #6923 | semidirect |
| 146. C61 | #23196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462599 | 2 |
| #21461978 | 2 |
| #21461821 | 2 |
| #21461621 | 2 |
| #21456248 | 2 |
| #23196 | 61 |