Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#16839585 | C2 | semidirect |
| 4. #21446600 | C2 | semidirect |
| 5. #21443930 | C2 | semidirect |
| 6. #21443906 | C2 | semidirect |
| 23. C61×#362 | C4 | semidirect |
| 24. C61×#361 | C4 | semidirect |
| 165. #362 | Dic61 | semidirect |
| 166. #361 | Dic61 | semidirect |
| 169. C61 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454736 | 2 |
| C2×#16839585 | 2 |
| C2×#16839572 | 2 |
| #21446600 | 2 |
| #21443930 | 2 |
| #21443906 | 2 |
| C61×#2148 | 2 |
| #12952 | 61 |