Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1220 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 220 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. #21462421 | C2 | semidirect |
| 2. #21462098 | C2 | semidirect |
| 3. #21462090 | C2 | semidirect |
| 7. #16840741 | C22 | semidirect |
| 8. #16840668 | C22 | semidirect |
| 9. #16840666 | C22 | semidirect |
| 13. #16840333 | C4 | semidirect |
| 16. C2×#14519764 | C4 | semidirect |
| 17. #41×Dic61 | C4 | semidirect |
| 18. C2×H(5,𝔽2)×C61 | C4 | semidirect |
| 143. C2×H(5,𝔽2) | #6923 | semidirect |
| 156. C61 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462421 | 2 |
| #21462098 | 2 |
| #21462090 | 2 |
| #21459607 | 2 |
| #33362 | 61 |