Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 2. #21454831 | C2 | semidirect |
| 3. #21445632 | C2 | semidirect |
| 4. #21444410 | C2 | semidirect |
| 5. #21444328 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 7. C61×#1291 | C2 | semidirect |
| 11. #16840048 | C4 | semidirect |
| 12. #16840043 | C4 | semidirect |
| 13. #16839963 | C4 | semidirect |
| 14. #16839958 | C4 | semidirect |
| 203. #1291 | D61 | semidirect |
| 235. C61 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455971 | 2 |
| #21454831 | 2 |
| #21445632 | 2 |
| #21444410 | 2 |
| #21444328 | 2 |
| #21443711 | 2 |
| C61×#1291 | 2 |
| #9161 | 61 |