Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 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. #70831 | C2 | semidirect |
| 4. #70812 | C2 | semidirect |
| 6. C3×#1307 | C2 | semidirect |
| 7. #67710 | C2 | semidirect |
| 39. #1307 | D3 | semidirect |
| 365. C3 | #9352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79329 | 2 |
| #79061 | 2 |
| #70831 | 2 |
| #70812 | 2 |
| #70798 | 2 |
| C3×#1307 | 2 |
| #67710 | 2 |
| #9352 | 3 |