Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21454806 | C2 | semidirect |
| 2. #21444450 | C2 | semidirect |
| 3. #21444262 | C2 | semidirect |
| 4. #21444160 | C2 | semidirect |
| 5. #21443731 | C2 | semidirect |
| 6. #21443692 | C2 | semidirect |
| 239. C61 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454806 | 2 |
| #21444450 | 2 |
| #21444262 | 2 |
| #21444160 | 2 |
| #21443731 | 2 |
| #21443692 | 2 |
| C61×#3114 | 2 |
| #9532 | 61 |