Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1254 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 3. C3×#1822 | C2 | semidirect |
| 4. #71589 | C2 | semidirect |
| 5. #69990 | C2 | semidirect |
| 6. #68993 | C2 | semidirect |
| 28. #1822 | D3 | semidirect |
| 277. C3 | #21756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5526 | 2 |
| #78630 | 2 |
| C3×#1822 | 2 |
| #71589 | 2 |
| #69990 | 2 |
| #68993 | 2 |
| #21756 | 3 |