Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
434 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21457125 | C2 | semidirect |
| 2. #21447731 | C2 | semidirect |
| 3. #21447127 | C2 | semidirect |
| 4. #21443829 | C2 | semidirect |
| 5. #21443828 | C2 | semidirect |
| 6. #21443758 | C2 | semidirect |
| 7. C61×#2184 | C2 | semidirect |
| 149. C2×Dic61 | D16 | semidirect |
| 186. #2184 | D61 | semidirect |
| 218. C61 | #12158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457125 | 2 |
| #21447731 | 2 |
| #21447127 | 2 |
| #21443829 | 2 |
| #21443828 | 2 |
| #21443758 | 2 |
| C61×#2184 | 2 |
| #12158 | 61 |