Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2140 | C2 | semidirect |
| 3. C2×#4563 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. #70662 | C2 | semidirect |
| 6. #70652 | C2 | semidirect |
| 7. #67810 | C2 | semidirect |
| 30. #2140 | D3 | semidirect |
| 61. C3×#107 | D4 | semidirect |
| 167. #107 | #67 | semidirect |
| 326. C3 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5151 | 2 |
| C3×#2140 | 2 |
| C2×#4563 | 2 |
| C2×#4516 | 2 |
| #70662 | 2 |
| #70652 | 2 |
| #67810 | 2 |
| #13413 | 3 |