Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#16839582 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. #21447536 | C2 | semidirect |
| 5. #21447535 | C2 | semidirect |
| 6. #21445701 | C2 | semidirect |
| 7. C2×C61×#361 | C2 | semidirect |
| 13. #16840137 | C4 | semidirect |
| 46. #14519711 | D4 | semidirect |
| 65. #108×C61 | D4 | semidirect |
| 170. C2×#361 | D61 | semidirect |
| 198. C61 | #13261 | semidirect |
| 232. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840137 | 2 |
| C2×#16839582 | 2 |
| C2×#16839574 | 2 |
| #21447536 | 2 |
| #21447535 | 2 |
| #21445701 | 2 |
| C2×C61×#361 | 2 |
| #13261 | 61 |