Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1220 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 311 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 |
|---|---|---|
| 1. #21454283 | C2 | semidirect |
| 2. #21447491 | C2 | semidirect |
| 3. #21447484 | C2 | semidirect |
| 7. #16839736 | C22 | semidirect |
| 8. #16839557 | C22 | semidirect |
| 9. #16839555 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C61 | C4 | semidirect |
| 14. C61×#536 | C4 | semidirect |
| 17. C2×#124×C61 | C4 | semidirect |
| 18. C4×#41×C61 | C4 | semidirect |
| 143. C2×H(5,𝔽2) | Dic61 | semidirect |
| 146. #536 | Dic61 | semidirect |
| 149. C2×#124 | Dic61 | semidirect |
| 151. C4×#41 | Dic61 | semidirect |
| 156. C61 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454283 | 2 |
| #21447491 | 2 |
| #21447484 | 2 |
| C61×#3500 | 2 |
| #33362 | 61 |