Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
232 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. C2×C3×Q64 | C2 | semidirect |
| 3. #71499 | C2 | semidirect |
| 4. C2×#4522 | C2 | semidirect |
| 7. #67589 | C2 | semidirect |
| 25. C2×Q64 | D3 | semidirect |
| 191. C3 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q64 | 2 |
| #71500 | 2 |
| #71499 | 2 |
| C2×#4522 | 2 |
| C2×#4521 | 2 |
| C2×#4449 | 2 |
| #67589 | 2 |
| #13730 | 3 |