Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
690 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 109 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×#3206 | C2 | semidirect |
| 3. C2×#5085 | C2 | semidirect |
| 4. #71802 | C2 | semidirect |
| 5. #71790 | C2 | semidirect |
| 6. #70774 | C2 | semidirect |
| 7. #67739 | C2 | semidirect |
| 30. #3206 | D3 | semidirect |
| 146. #208 | SD16 | semidirect |
| 368. C3 | #10146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3206 | 2 |
| #83287 | 2 |
| C2×#5085 | 2 |
| #71802 | 2 |
| #71790 | 2 |
| #70774 | 2 |
| #67739 | 2 |
| #10146 | 3 |