Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21447701 | C2 | semidirect |
| 3. #21444022 | C2 | semidirect |
| 4. #21444003 | C2 | semidirect |
| 5. #21444002 | C2 | semidirect |
| 6. #21443953 | C2 | semidirect |
| 7. C61×#2178 | C2 | semidirect |
| 10. #16839602 | C4 | semidirect |
| 11. #16839600 | C4 | semidirect |
| 12. #16839599 | C4 | semidirect |
| 13. #16839597 | C4 | semidirect |
| 90. #2178 | D61 | semidirect |
| 114. C61 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448126 | 2 |
| #21447701 | 2 |
| #21444022 | 2 |
| #21444003 | 2 |
| #21444002 | 2 |
| #21443953 | 2 |
| C61×#2178 | 2 |
| #13656 | 61 |