Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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. #83216 | C2 | semidirect |
| 2. C2×#5087 | C2 | semidirect |
| 4. C3×#1548 | C2 | semidirect |
| 5. #70783 | C2 | semidirect |
| 6. #70758 | C2 | semidirect |
| 7. #67714 | C2 | semidirect |
| 35. #1548 | D3 | semidirect |
| 409. C3 | #10188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83216 | 2 |
| C2×#5087 | 2 |
| #79055 | 2 |
| C3×#1548 | 2 |
| #70783 | 2 |
| #70758 | 2 |
| #67714 | 2 |
| #10188 | 3 |