Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21445571 | C2 | semidirect |
| 3. #21444580 | C2 | semidirect |
| 4. #21444431 | C2 | semidirect |
| 5. #21444430 | C2 | semidirect |
| 6. #21444326 | C2 | semidirect |
| 7. C61×#1505 | C2 | semidirect |
| 9. #16840165 | C4 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 12. #16840108 | C4 | semidirect |
| 185. #1505 | D61 | semidirect |
| 215. C61 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456394 | 2 |
| #21445571 | 2 |
| #21444580 | 2 |
| #21444431 | 2 |
| #21444430 | 2 |
| #21444326 | 2 |
| C61×#1505 | 2 |
| #9764 | 61 |