Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21458969 | C2 | semidirect |
| 2. #21458968 | C2 | semidirect |
| 3. #21448139 | C2 | semidirect |
| 4. #21448138 | C2 | semidirect |
| 5. #21448135 | C2 | semidirect |
| 6. #21448127 | C2 | semidirect |
| 7. #21448126 | C2 | semidirect |
| 8. C2×#16839602 | C2 | semidirect |
| 9. Q64×D61 | C2 | semidirect |
| 10. #21448114 | C2 | semidirect |
| 11. C61×#2264 | C2 | semidirect |
| 160. #2264 | D61 | semidirect |
| 200. C61 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458969 | 2 |
| #21458968 | 2 |
| #21448139 | 2 |
| #21448138 | 2 |
| #21448135 | 2 |
| #21448127 | 2 |
| #21448126 | 2 |
| C2×#16839602 | 2 |
| Q64×D61 | 2 |
| #21448114 | 2 |
| C61×#2264 | 2 |
| #33984 | 61 |