Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #21454687 | C2 | semidirect |
| 4. #21447883 | C2 | semidirect |
| 5. #21447867 | C2 | semidirect |
| 6. #21447577 | C2 | semidirect |
| 7. #21447539 | C2 | semidirect |
| 9. C22×Q32×C61 | C2 | semidirect |
| 169. C22×Q32 | D61 | semidirect |
| 206. C61 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840203 | 2 |
| #21456308 | 2 |
| #21454687 | 2 |
| #21447883 | 2 |
| #21447867 | 2 |
| #21447577 | 2 |
| #21447539 | 2 |
| #21447527 | 2 |
| C22×Q32×C61 | 2 |
| #33588 | 61 |