Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 84 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. #21462722 | C2 | semidirect |
| 3. #21461161 | C2 | semidirect |
| 5. #21460684 | C2 | semidirect |
| 6. #21460664 | C2 | semidirect |
| 242. C61 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462722 | 2 |
| #21461280 | 2 |
| #21461161 | 2 |
| #21461090 | 2 |
| #21460684 | 2 |
| #21460664 | 2 |
| C2×#16839986 | 2 |
| #9244 | 61 |