Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21447621 | C2 | semidirect |
| 3. #334×D61 | C2 | semidirect |
| 4. #21443871 | C2 | semidirect |
| 5. #21443863 | C2 | semidirect |
| 6. #21443861 | C2 | semidirect |
| 7. C61×#1363 | C2 | semidirect |
| 149. #1363 | D61 | semidirect |
| 176. C61 | #11945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456391 | 2 |
| #21447621 | 2 |
| #334×D61 | 2 |
| #21443871 | 2 |
| #21443863 | 2 |
| #21443861 | 2 |
| C61×#1363 | 2 |
| #11945 | 61 |