Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
430 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C3×#362 | C2 | semidirect |
| 3. C2×#4564 | C2 | semidirect |
| 5. #70701 | C2 | semidirect |
| 7. #67815 | C2 | semidirect |
| 29. C2×#362 | D3 | semidirect |
| 354. C3 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83881 | 2 |
| C2×C3×#362 | 2 |
| C2×#4564 | 2 |
| #71439 | 2 |
| #70701 | 2 |
| C2×#4497 | 2 |
| #67815 | 2 |
| #13412 | 3 |