Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
768 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 148 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. #21460907 | C2 | semidirect |
| 7. #16840741 | C4 | semidirect |
| 10. C2×#14519835 | C4 | semidirect |
| 12. C22×#11758194 | C4 | semidirect |
| 14. #16839728 | C4 | semidirect |
| 17. C22×M16×C61 | C4 | semidirect |
| 28. #14519835 | C2×C4 | semidirect |
| 43. C2×#11758194 | C2×C4 | semidirect |
| 51. C22×C8×C61 | C2×C4 | semidirect |
| 194. C22×M16 | #6923 | semidirect |
| 206. C61 | #12577 | semidirect |
| 227. C22×C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840741 | 2 |
| #21460907 | 2 |
| #21454263 | 2 |
| #12577 | 61 |