Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #21445570 | C2 | semidirect |
| 3. #21444435 | C2 | semidirect |
| 5. #21444332 | C2 | semidirect |
| 7. C61×#1568 | C2 | semidirect |
| 10. #16840160 | C4 | semidirect |
| 11. #16840135 | C4 | semidirect |
| 12. #16840113 | C4 | semidirect |
| 13. #16840109 | C4 | semidirect |
| 174. #1568 | D61 | semidirect |
| 207. C61 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456378 | 2 |
| #21445570 | 2 |
| #21444435 | 2 |
| #21444431 | 2 |
| #21444332 | 2 |
| #21444328 | 2 |
| C61×#1568 | 2 |
| #9766 | 61 |