Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
512 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 109 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×#4700 | C2 | semidirect |
| 3. C3×#1970 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. #70598 | C2 | semidirect |
| 6. #67723 | C2 | semidirect |
| 7. #67658 | C2 | semidirect |
| 18. #5147 | C4 | semidirect |
| 33. #1970 | D3 | semidirect |
| 139. Dic12 | C22⋊C4 | semidirect |
| 141. D24 | C22⋊C4 | semidirect |
| 363. C3 | #13029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5147 | 2 |
| C2×#4700 | 2 |
| C3×#1970 | 2 |
| C2×#4563 | 2 |
| #70598 | 2 |
| #67723 | 2 |
| #67658 | 2 |
| #13029 | 3 |