Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16839574 | C2 | semidirect |
| 3. #21447547 | C2 | semidirect |
| 4. #21446729 | C2 | semidirect |
| 5. #21443922 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 7. C61×#2957 | C2 | semidirect |
| 11. C2×#14519720 | C4 | semidirect |
| 12. C2×#14519718 | C4 | semidirect |
| 166. #2957 | D61 | semidirect |
| 197. C61 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C2×#16839574 | 2 |
| #21447547 | 2 |
| #21446729 | 2 |
| #21443922 | 2 |
| #21443905 | 2 |
| C61×#2957 | 2 |
| #13036 | 61 |