Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#16839498 | C2 | semidirect |
| 4. #21444184 | C2 | semidirect |
| 5. #21443706 | C2 | semidirect |
| 6. #21443662 | C2 | semidirect |
| 10. #16840090 | C4 | semidirect |
| 11. #16840073 | C4 | semidirect |
| 15. #16839917 | C4 | semidirect |
| 16. #16839900 | C4 | semidirect |
| 268. C61 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456596 | 2 |
| #21454875 | 2 |
| C2×#16839498 | 2 |
| #21444184 | 2 |
| #21443706 | 2 |
| #21443662 | 2 |
| C61×#1504 | 2 |
| #9263 | 61 |