Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 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. #21454949 | C2 | semidirect |
| 3. C4×#14519705 | C2 | semidirect |
| 4. #21444236 | C2 | semidirect |
| 5. #21443708 | C2 | semidirect |
| 6. #21443652 | C2 | semidirect |
| 7. C61×#1962 | C2 | semidirect |
| 10. #16840054 | C4 | semidirect |
| 11. #16840049 | C4 | semidirect |
| 12. #16839959 | C4 | semidirect |
| 13. #16839954 | C4 | semidirect |
| 179. Dic122 | #104 | semidirect |
| 213. #1962 | D61 | semidirect |
| 249. C61 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455873 | 2 |
| #21454949 | 2 |
| C4×#14519705 | 2 |
| #21444236 | 2 |
| #21443708 | 2 |
| #21443652 | 2 |
| C61×#1962 | 2 |
| #8970 | 61 |