Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 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. C3×#3135 | C2 | semidirect |
| 2. #83355 | C2 | semidirect |
| 4. #71838 | C2 | semidirect |
| 5. #71814 | C2 | semidirect |
| 6. #69823 | C2 | semidirect |
| 7. #67661 | C2 | semidirect |
| 34. #3135 | D3 | semidirect |
| 385. C3 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3135 | 2 |
| #83355 | 2 |
| #83302 | 2 |
| #71838 | 2 |
| #71814 | 2 |
| #69823 | 2 |
| #67661 | 2 |
| #10219 | 3 |