Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #83329 | C2 | semidirect |
| 3. C3×#1518 | C2 | semidirect |
| 6. #67740 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 13. #5088 | C4 | semidirect |
| 14. #5085 | C4 | semidirect |
| 32. #1518 | D3 | semidirect |
| 137. C2×C3⋊C8 | SD16 | semidirect |
| 346. C3 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83355 | 2 |
| #83329 | 2 |
| C3×#1518 | 2 |
| #70774 | 2 |
| #69553 | 2 |
| #67740 | 2 |
| #67631 | 2 |
| #9294 | 3 |