Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #71427 | C2 | semidirect |
| 5. #70707 | C2 | semidirect |
| 6. #67814 | C2 | semidirect |
| 7. #67735 | C2 | semidirect |
| 21. C3×#361 | C4 | semidirect |
| 49. C3×M32 | C2×C4 | semidirect |
| 52. C3×#108 | C2×C4 | semidirect |
| 78. #361 | Dic3 | semidirect |
| 136. M32 | C2×Dic3 | semidirect |
| 143. #108 | C2×Dic3 | semidirect |
| 269. C3 | #12953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83823 | 2 |
| C2×C3×#361 | 2 |
| C2×#4563 | 2 |
| #71427 | 2 |
| #70707 | 2 |
| #67814 | 2 |
| #67735 | 2 |
| #12953 | 3 |