Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21447635 | C2 | semidirect |
| 3. #21443812 | C2 | semidirect |
| 5. #21443806 | C2 | semidirect |
| 7. C61×#1747 | C2 | semidirect |
| 9. #16840160 | C4 | semidirect |
| 10. #16840146 | C4 | semidirect |
| 15. #16839875 | C4 | semidirect |
| 16. #16839870 | C4 | semidirect |
| 143. #1747 | D61 | semidirect |
| 171. C61 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456436 | 2 |
| #21447635 | 2 |
| #21443812 | 2 |
| #21443809 | 2 |
| #21443806 | 2 |
| #21443803 | 2 |
| C61×#1747 | 2 |
| #11769 | 61 |