Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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. C3×#2252 | C2 | semidirect |
| 3. #71385 | C2 | semidirect |
| 5. #69321 | C2 | semidirect |
| 7. #69044 | C2 | semidirect |
| 29. #2252 | D3 | semidirect |
| 55. D3×C16 | Q8 | semidirect |
| 214. C3 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81938 | 2 |
| C3×#2252 | 2 |
| #71385 | 2 |
| #69325 | 2 |
| #69321 | 2 |
| C4×D3×C16 | 2 |
| #69044 | 2 |
| #33726 | 3 |