Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 23. #16839579 | C4 | semidirect |
| 24. #16839578 | C4 | semidirect |
| 25. #16839577 | C4 | semidirect |
| 26. C61×#362 | C4 | semidirect |
| 174. #362 | #6923 | semidirect |
| 176. C61 | #13139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#365 | 2 |
| D61⋊#362 | 2 |
| #21461967 | 2 |
| #21461640 | 2 |
| #21460885 | 2 |
| #21460865 | 2 |
| #362×D61 | 2 |
| #13139 | 61 |