Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 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. #78605 | C2 | semidirect |
| 3. #69921 | C2 | semidirect |
| 4. #69398 | C2 | semidirect |
| 5. C2×#4451 | C2 | semidirect |
| 6. C3×#1280 | C2 | semidirect |
| 7. #67680 | C2 | semidirect |
| 21. #4735 | C4 | semidirect |
| 23. #4732 | C4 | semidirect |
| 24. #4731 | C4 | semidirect |
| 28. #4722 | C4 | semidirect |
| 42. #1280 | D3 | semidirect |
| 480. C3 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78613 | 2 |
| #78605 | 2 |
| #69921 | 2 |
| #69398 | 2 |
| C2×#4451 | 2 |
| C3×#1280 | 2 |
| #67680 | 2 |
| #9264 | 3 |