Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2337 | C2 | semidirect |
| 3. #71718 | C2 | semidirect |
| 4. #69564 | C2 | semidirect |
| 5. #69492 | C2 | semidirect |
| 6. #67633 | C2 | semidirect |
| 7. #67621 | C2 | semidirect |
| 21. #5058 | C4 | semidirect |
| 23. #5055 | C4 | semidirect |
| 33. #2337 | D3 | semidirect |
| 64. #874 | C2×C4 | semidirect |
| 67. #869 | C2×C4 | semidirect |
| 85. #803 | C2×C4 | semidirect |
| 435. C3 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2337 | 2 |
| #82947 | 2 |
| #71718 | 2 |
| #69564 | 2 |
| #69492 | 2 |
| #67633 | 2 |
| #67621 | 2 |
| #9381 | 3 |