Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
316 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21448094 | C2 | semidirect |
| 4. #21445214 | C2 | semidirect |
| 5. #21443875 | C2 | semidirect |
| 6. #21443799 | C2 | semidirect |
| 62. D8×C61 | Q16 | semidirect |
| 151. C61 | #12404 | semidirect |
| 190. D8 | Dic244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic122 | 2 |
| #21448094 | 2 |
| #21447956 | 2 |
| #21445214 | 2 |
| #21443875 | 2 |
| #21443799 | 2 |
| C61×#1331 | 2 |
| #12404 | 61 |