Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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. #83130 | C2 | semidirect |
| 3. #71761 | C2 | semidirect |
| 4. #71760 | C2 | semidirect |
| 5. #71755 | C2 | semidirect |
| 6. #67755 | C2 | semidirect |
| 7. #67749 | C2 | semidirect |
| 11. C3×#496 | C4 | semidirect |
| 12. C3×#490 | C4 | semidirect |
| 92. #496 | Dic3 | semidirect |
| 93. #490 | Dic3 | semidirect |
| 423. C3 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3217 | 2 |
| #83130 | 2 |
| #71761 | 2 |
| #71760 | 2 |
| #71755 | 2 |
| #67755 | 2 |
| #67749 | 2 |
| #9378 | 3 |