Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1088 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×C4×C22⋊Dic61 | C2 | semidirect |
| 2. #21445729 | C2 | semidirect |
| 3. C2×#16839496 | C2 | semidirect |
| 4. #21443697 | C2 | semidirect |
| 14. C2×#121×C61 | C4 | semidirect |
| 19. C61×#380 | C4 | semidirect |
| 31. #14519684 | D4 | semidirect |
| 212. C2×#121 | Dic61 | semidirect |
| 221. #380 | Dic61 | semidirect |
| 226. C61 | #9150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic61 | 2 |
| #21445729 | 2 |
| C2×#16839496 | 2 |
| #21443697 | 2 |
| C61×#2847 | 2 |
| #9150 | 61 |