Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21458953 | C2 | semidirect |
| 2. C2×#16840198 | C2 | semidirect |
| 3. #21447555 | C2 | semidirect |
| 4. #21447535 | C2 | semidirect |
| 5. #21446717 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 7. C61×#3155 | C2 | semidirect |
| 38. C2×Dic244 | D4 | semidirect |
| 40. C2×D488 | D4 | semidirect |
| 51. #14519717 | D4 | semidirect |
| 53. C2×#11758185 | D4 | semidirect |
| 213. #3155 | D61 | semidirect |
| 250. C61 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| C2×#16840198 | 2 |
| #21447555 | 2 |
| #21447535 | 2 |
| #21446717 | 2 |
| #21443905 | 2 |
| C61×#3155 | 2 |
| #13334 | 61 |