Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21447584 | C2 | semidirect |
| 5. #21445944 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 11. #16839873 | C4 | semidirect |
| 12. #16839868 | C4 | semidirect |
| 152. #1383 | D61 | semidirect |
| 175. C61 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454702 | 2 |
| #21447584 | 2 |
| #21447556 | 2 |
| #21447546 | 2 |
| #21445944 | 2 |
| #21443926 | 2 |
| C61×#1383 | 2 |
| #12828 | 61 |