Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
246 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 70 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. #21461417 | C2 | semidirect |
| 2. #21461415 | C2 | semidirect |
| 3. #21460845 | C2 | semidirect |
| 4. #21460778 | C2 | semidirect |
| 5. #21460777 | C2 | semidirect |
| 6. #21460736 | C2 | semidirect |
| 35. #14519718 | C8 | semidirect |
| 55. D8×C61 | C2×C8 | semidirect |
| 64. D488 | C2×C8 | semidirect |
| 67. #11758185 | C2×C8 | semidirect |
| 131. C61 | #12067 | semidirect |
| 160. D8 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461417 | 2 |
| #21461415 | 2 |
| #21460845 | 2 |
| #21460778 | 2 |
| #21460777 | 2 |
| #21460736 | 2 |
| #21447692 | 2 |
| #12067 | 61 |