Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21445855 | C2 | semidirect |
| 3. #21445597 | C2 | semidirect |
| 4. #21444338 | C2 | semidirect |
| 5. #21444184 | C2 | semidirect |
| 8. C22×#11758200 | C4 | semidirect |
| 16. C2×#14519708 | C4 | semidirect |
| 17. C2×#14519700 | C4 | semidirect |
| 18. C2×#14519698 | C4 | semidirect |
| 246. C61 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839989 | 2 |
| #21445855 | 2 |
| #21445597 | 2 |
| #21444338 | 2 |
| #21444184 | 2 |
| #21444179 | 2 |
| C61×#1507 | 2 |
| #9816 | 61 |