Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21445960 | C2 | semidirect |
| 3. #21444550 | C2 | semidirect |
| 5. #21444433 | C2 | semidirect |
| 6. #21443729 | C2 | semidirect |
| 180. C61 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457206 | 2 |
| #21445960 | 2 |
| #21444550 | 2 |
| #21444541 | 2 |
| #21444433 | 2 |
| #21443729 | 2 |
| C61×#1530 | 2 |
| #10527 | 61 |