Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. D61⋊#361 | C2 | semidirect |
| 3. #21462135 | C2 | semidirect |
| 4. #21461980 | C2 | semidirect |
| 5. #21460889 | C2 | semidirect |
| 6. #21460868 | C2 | semidirect |
| 24. C2×#14519720 | C4 | semidirect |
| 25. C2×D976 | C4 | semidirect |
| 26. C2×#14519718 | C4 | semidirect |
| 28. C2×SD32×C61 | C4 | semidirect |
| 200. C2×SD32 | #6923 | semidirect |
| 215. C61 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462599 | 2 |
| D61⋊#361 | 2 |
| #21462135 | 2 |
| #21461980 | 2 |
| #21460889 | 2 |
| #21460868 | 2 |
| C2×#16840199 | 2 |
| #13036 | 61 |