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. #21447573 | C2 | semidirect |
| 3. #346×D61 | C2 | semidirect |
| 4. #21443778 | C2 | semidirect |
| 5. #21443777 | C2 | semidirect |
| 6. #21443776 | C2 | semidirect |
| 7. C61×#1330 | C2 | semidirect |
| 168. #1330 | D61 | semidirect |
| 194. C61 | #11588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454528 | 2 |
| #21447573 | 2 |
| #346×D61 | 2 |
| #21443778 | 2 |
| #21443777 | 2 |
| #21443776 | 2 |
| C61×#1330 | 2 |
| #11588 | 61 |