Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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. #71428 | C2 | semidirect |
| 7. #67729 | C2 | semidirect |
| 30. C2×#362 | D3 | semidirect |
| 342. C3 | #13388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83887 | 2 |
| C2×C3×#362 | 2 |
| C2×#4564 | 2 |
| C2×#4515 | 2 |
| #71428 | 2 |
| #70721 | 2 |
| #67729 | 2 |
| #13388 | 3 |