Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 108 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. #21461612 | C2 | semidirect |
| 4. #21461035 | C2 | semidirect |
| 5. #21460716 | C2 | semidirect |
| 6. #21460711 | C2 | semidirect |
| 10. #16840797 | C4 | semidirect |
| 12. D4×#92420 | C4 | semidirect |
| 26. #16839509 | C4 | semidirect |
| 27. #16839507 | C4 | semidirect |
| 28. #16839506 | C4 | semidirect |
| 29. C61×#331 | C4 | semidirect |
| 206. #331 | #6923 | semidirect |
| 210. C61 | #8257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462541 | 2 |
| #21461612 | 2 |
| #21461199 | 2 |
| #21461035 | 2 |
| #21460716 | 2 |
| #21460711 | 2 |
| #21444465 | 2 |
| #8257 | 61 |