Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
314 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 6. C22×C3×C16 | C4 | semidirect |
| 15. #4549 | C4 | semidirect |
| 40. C22×C16 | Dic3 | semidirect |
| 70. #217 | C16 | semidirect |
| 227. C3 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊C16 | 2 |
| C8×#217 | 2 |
| C2×#4549 | 2 |
| #7199 | 3 |