Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
674 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 21. #16840160 | C4 | semidirect |
| 22. #16840159 | C4 | semidirect |
| 23. #16840158 | C4 | semidirect |
| 26. C61×#498 | C4 | semidirect |
| 139. #498 | #6923 | semidirect |
| 154. C61 | #22253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462314 | 2 |
| #21462003 | 2 |
| #21461882 | 2 |
| #21461881 | 2 |
| #21461741 | 2 |
| #21461537 | 2 |
| #498×D61 | 2 |
| #22253 | 61 |