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. #79341 | C2 | semidirect |
| 3. #70818 | C2 | semidirect |
| 4. #69487 | C2 | semidirect |
| 5. #69470 | C2 | semidirect |
| 6. C3×#1285 | C2 | semidirect |
| 7. #67755 | C2 | semidirect |
| 26. #4713 | C4 | semidirect |
| 27. #4712 | C4 | semidirect |
| 40. #1285 | 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 |
| #79341 | 2 |
| #70818 | 2 |
| #69487 | 2 |
| #69470 | 2 |
| C3×#1285 | 2 |
| #67755 | 2 |
| #9378 | 3 |