Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
726 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 207 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. #21446626 | C2 | semidirect |
| 2. #21445979 | C2 | semidirect |
| 3. C2×C8×#92418 | C2 | semidirect |
| 13. C61×#493 | C4 | semidirect |
| 57. C2×#92418 | D8 | semidirect |
| 78. C8×C61 | #102 | semidirect |
| 109. #493 | Dic61 | semidirect |
| 116. C61 | #9824 | semidirect |
| 181. C8 | #14519698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446626 | 2 |
| #21445979 | 2 |
| C2×C8×#92418 | 2 |
| C2×C61×#493 | 2 |
| #9824 | 61 |