Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #79289 | C2 | semidirect |
| 3. #70761 | C2 | semidirect |
| 4. #69859 | C2 | semidirect |
| 5. #69853 | C2 | semidirect |
| 6. C3×#1278 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 38. #1278 | D3 | semidirect |
| 388. C3 | #9069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79289 | 2 |
| #78467 | 2 |
| #70761 | 2 |
| #69859 | 2 |
| #69853 | 2 |
| C3×#1278 | 2 |
| #67656 | 2 |
| #9069 | 3 |