Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21454848 | C2 | semidirect |
| 2. C4×#14519694 | C2 | semidirect |
| 3. #21444417 | C2 | semidirect |
| 4. #21443683 | C2 | semidirect |
| 34. #14519688 | D4 | semidirect |
| 225. C61 | #9187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454848 | 2 |
| C4×#14519694 | 2 |
| #21444417 | 2 |
| #21443683 | 2 |
| C61×#2631 | 2 |
| #9187 | 61 |