Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #21448179 | C2 | semidirect |
| 3. #21444327 | C2 | semidirect |
| 4. #21444263 | C2 | semidirect |
| 5. #21443713 | C2 | semidirect |
| 6. #21443675 | C2 | semidirect |
| 7. C61×#1980 | C2 | semidirect |
| 11. #16840049 | C4 | semidirect |
| 12. #16839954 | C4 | semidirect |
| 45. C4⋊#92418 | C2×C4 | semidirect |
| 58. C4⋊Q8×C61 | C2×C4 | semidirect |
| 59. #127×C61 | C2×C4 | semidirect |
| 158. D244 | #104 | semidirect |
| 192. #1980 | D61 | semidirect |
| 225. C61 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D61 | semidirect |
| 233. #127 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455906 | 2 |
| #21448179 | 2 |
| #21444327 | 2 |
| #21444263 | 2 |
| #21443713 | 2 |
| #21443675 | 2 |
| C61×#1980 | 2 |
| #9325 | 61 |