Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21454804 | C2 | semidirect |
| 3. #21444394 | C2 | semidirect |
| 4. #21444365 | C2 | semidirect |
| 5. #21444237 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 7. C61×#1288 | C2 | semidirect |
| 10. #16840156 | C4 | semidirect |
| 11. #16840151 | C4 | semidirect |
| 12. #16840131 | C4 | semidirect |
| 13. #16840127 | C4 | semidirect |
| 204. #1288 | D61 | semidirect |
| 239. C61 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456858 | 2 |
| #21454804 | 2 |
| #21444394 | 2 |
| #21444365 | 2 |
| #21444237 | 2 |
| #21443680 | 2 |
| C61×#1288 | 2 |
| #9370 | 61 |