Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
666 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 666 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. #21454298 | C2 | semidirect |
| 3. #21447510 | C2 | semidirect |
| 4. #21447468 | C2 | semidirect |
| 5. #21443947 | C2 | semidirect |
| 6. #21443941 | C2 | semidirect |
| 7. C61×#1795 | C2 | semidirect |
| 8. C2×#14519802 | C4 | semidirect |
| 9. C22×#11758199 | C4 | semidirect |
| 16. #16839767 | C4 | semidirect |
| 17. #16839758 | C4 | semidirect |
| 251. #1795 | D61 | semidirect |
| 286. C61 | #13099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455087 | 2 |
| #21454298 | 2 |
| #21447510 | 2 |
| #21447468 | 2 |
| #21443947 | 2 |
| #21443941 | 2 |
| C61×#1795 | 2 |
| #13099 | 61 |