Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 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. #79016 | C2 | semidirect |
| 3. #70833 | C2 | semidirect |
| 4. #70818 | C2 | semidirect |
| 5. #70457 | C2 | semidirect |
| 6. C3×#1290 | C2 | semidirect |
| 7. #67749 | C2 | semidirect |
| 28. #4713 | C4 | semidirect |
| 29. #4712 | C4 | semidirect |
| 39. #1290 | D3 | semidirect |
| 423. C3 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79353 | 2 |
| #79016 | 2 |
| #70833 | 2 |
| #70818 | 2 |
| #70457 | 2 |
| C3×#1290 | 2 |
| #67749 | 2 |
| #9378 | 3 |