Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21457624 | C2 | semidirect |
| 2. #21447892 | C2 | semidirect |
| 3. #21445424 | C2 | semidirect |
| 4. #21443857 | C2 | semidirect |
| 5. #21443792 | C2 | semidirect |
| 6. #21443791 | C2 | semidirect |
| 7. C61×#2213 | C2 | semidirect |
| 141. #2213 | D61 | semidirect |
| 168. C61 | #12311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457624 | 2 |
| #21447892 | 2 |
| #21445424 | 2 |
| #21443857 | 2 |
| #21443792 | 2 |
| #21443791 | 2 |
| C61×#2213 | 2 |
| #12311 | 61 |