Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 102 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. #21462036 | C2 | semidirect |
| 4. #21461639 | C2 | semidirect |
| 5. #21460898 | C2 | semidirect |
| 6. #21460888 | C2 | semidirect |
| 13. #16840681 | C4 | semidirect |
| 14. #16840680 | C4 | semidirect |
| 15. #16840677 | C4 | semidirect |
| 16. #16840676 | C4 | semidirect |
| 221. C61 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462147 | 2 |
| #21462133 | 2 |
| #21462036 | 2 |
| #21461639 | 2 |
| #21460898 | 2 |
| #21460888 | 2 |
| #444×D61 | 2 |
| #12651 | 61 |