Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #21444413 | C2 | semidirect |
| 5. #21444332 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 7. C61×#1291 | C2 | semidirect |
| 11. #16840058 | C4 | semidirect |
| 12. #16840053 | C4 | semidirect |
| 13. #16839973 | C4 | semidirect |
| 14. #16839968 | C4 | semidirect |
| 196. #1291 | D61 | semidirect |
| 227. C61 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455982 | 2 |
| #21454831 | 2 |
| #21445632 | 2 |
| #21444413 | 2 |
| #21444332 | 2 |
| #21443711 | 2 |
| C61×#1291 | 2 |
| #9159 | 61 |