Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70787 | C2 | semidirect |
| 4. C2×#4465 | C2 | semidirect |
| 6. C3×#1281 | C2 | semidirect |
| 7. #67742 | C2 | semidirect |
| 42. #1281 | D3 | semidirect |
| 380. C3 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79279 | 2 |
| #79274 | 2 |
| #70787 | 2 |
| C2×#4465 | 2 |
| #69799 | 2 |
| C3×#1281 | 2 |
| #67742 | 2 |
| #9266 | 3 |