Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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×#361 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #71440 | C2 | semidirect |
| 5. C2×#4511 | C2 | semidirect |
| 6. #70702 | C2 | semidirect |
| 7. C2×#4495 | C2 | semidirect |
| 16. #5151 | C4 | semidirect |
| 30. C2×#361 | D3 | semidirect |
| 64. C3×#108 | D4 | semidirect |
| 65. #818 | D4 | semidirect |
| 173. #108 | #67 | semidirect |
| 338. C3 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5151 | 2 |
| C2×C3×#361 | 2 |
| #72033 | 2 |
| #71440 | 2 |
| C2×#4511 | 2 |
| #70702 | 2 |
| C2×#4495 | 2 |
| #13261 | 3 |