Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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 |
|---|---|---|
| 3. C3×#1713 | C2 | semidirect |
| 4. #71362 | C2 | semidirect |
| 5. #71298 | C2 | semidirect |
| 6. #68065 | C2 | semidirect |
| 30. #1713 | D3 | direct (N × H) |
| 91. D3×C8 | Q16 | semidirect |
| 128. C3×C8 | C2×Q16 | semidirect |
| 130. C3⋊C8 | C2×Q16 | semidirect |
| 178. C8 | D3×Q16 | semidirect |
| 181. D3 | #1713 | direct (N × H) |
| 191. C3 | C2×#1713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#500 | 2 |
| D3×#494 | 2 |
| C3×#1713 | 2 |
| #71362 | 2 |
| #71298 | 2 |
| #68065 | 2 |
| D3×C82 | 2 |
| C2×#1713 | 3 |