Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
564 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 110 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. #21462669 | C2 | semidirect |
| 2. #21461120 | C2 | semidirect |
| 3. #21461118 | C2 | semidirect |
| 4. #21461059 | C2 | semidirect |
| 5. #21460659 | C2 | semidirect |
| 6. #21460645 | C2 | semidirect |
| 46. C2×#11758199 | C8 | semidirect |
| 75. C2×D4×C61 | C2×C8 | semidirect |
| 116. C2×#92418 | C2×C8 | semidirect |
| 221. C61 | #9089 | semidirect |
| 276. C2×D4 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462669 | 2 |
| #21461120 | 2 |
| #21461118 | 2 |
| #21461059 | 2 |
| #21460659 | 2 |
| #21460645 | 2 |
| C2×#16839871 | 2 |
| #9089 | 61 |