Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
496 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21456384 | C2 | semidirect |
| 2. #21447986 | C2 | semidirect |
| 3. #21447978 | C2 | semidirect |
| 4. #21447930 | C2 | semidirect |
| 5. #21447927 | C2 | semidirect |
| 6. #21447880 | C2 | semidirect |
| 7. #21447872 | C2 | semidirect |
| 8. #21447574 | C2 | semidirect |
| 178. C61 | #33822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456384 | 2 |
| #21447986 | 2 |
| #21447978 | 2 |
| #21447930 | 2 |
| #21447927 | 2 |
| #21447880 | 2 |
| #21447872 | 2 |
| #21447574 | 2 |
| C61×#2218 | 2 |
| #33822 | 61 |