Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 93 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. #78516 | C2 | semidirect |
| 3. #70806 | C2 | semidirect |
| 4. #70798 | C2 | semidirect |
| 5. #69853 | C2 | semidirect |
| 6. C3×#1291 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 40. #1291 | D3 | semidirect |
| 394. C3 | #9311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79347 | 2 |
| #78516 | 2 |
| #70806 | 2 |
| #70798 | 2 |
| #69853 | 2 |
| C3×#1291 | 2 |
| #67751 | 2 |
| #9311 | 3 |