Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21461539 | C2 | semidirect |
| 4. #21461017 | C2 | semidirect |
| 5. #21460713 | C2 | semidirect |
| 6. #21460708 | C2 | semidirect |
| 8. #16840813 | C4 | semidirect |
| 9. Q8×#92420 | C4 | semidirect |
| 10. #16840797 | C4 | semidirect |
| 13. D4×#92420 | C4 | semidirect |
| 29. #16839503 | C4 | semidirect |
| 30. #16839503 | C4 | semidirect |
| 31. #16839502 | C4 | semidirect |
| 32. C61×#329 | C4 | semidirect |
| 205. #329 | #6923 | semidirect |
| 210. C61 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462633 | 2 |
| #21461539 | 2 |
| #21461191 | 2 |
| #21461017 | 2 |
| #21460713 | 2 |
| #21460708 | 2 |
| #21444404 | 2 |
| #8250 | 61 |