Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21448042 | C2 | semidirect |
| 2. #21447966 | C2 | semidirect |
| 3. #21445218 | C2 | semidirect |
| 4. #21443865 | C2 | semidirect |
| 5. #21443780 | C2 | semidirect |
| 6. D4⋊#11758185 | C2 | semidirect |
| 8. #16840167 | C22 | semidirect |
| 11. C4⋊#11758185 | C22 | semidirect |
| 14. C4×#11758185 | C22 | semidirect |
| 15. #16839515 | C22 | semidirect |
| 174. C61 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448042 | 2 |
| #21447966 | 2 |
| #21445218 | 2 |
| #21443865 | 2 |
| #21443780 | 2 |
| D4⋊#11758185 | 2 |
| D4×D8×C61 | 2 |
| #12372 | 61 |