Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 19. #16839590 | C4 | semidirect |
| 20. #16839589 | C4 | semidirect |
| 21. #16839587 | C4 | semidirect |
| 22. C61×#366 | C4 | semidirect |
| 149. #366 | #6923 | semidirect |
| 152. C61 | #13118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461924 | 2 |
| #21461626 | 2 |
| #21460893 | 2 |
| #21460890 | 2 |
| #21460884 | 2 |
| #21460859 | 2 |
| #21447604 | 2 |
| #13118 | 61 |