Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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. #21462220 | C2 | semidirect |
| 2. #21460983 | C2 | semidirect |
| 3. #21460971 | C2 | semidirect |
| 4. #21460925 | C2 | semidirect |
| 12. #16839599 | C4 | semidirect |
| 13. D1952 | C4 | semidirect |
| 15. C61×Q64 | C4 | semidirect |
| 69. Q64 | #6923 | semidirect |
| 77. C61 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462220 | 2 |
| #21460983 | 2 |
| #21460971 | 2 |
| #21460925 | 2 |
| #21448129 | 2 |
| #13656 | 61 |