Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 69 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. #81789 | C2 | semidirect |
| 2. C3×#2246 | C2 | semidirect |
| 3. #71293 | C2 | semidirect |
| 4. #71282 | C2 | semidirect |
| 5. #67790 | C2 | semidirect |
| 6. #67504 | C2 | semidirect |
| 7. #67503 | C2 | semidirect |
| 13. C3×#493 | C22 | semidirect |
| 21. C3×C4×C16 | C22 | semidirect |
| 24. C4⋊(C3⋊C16) | C22 | semidirect |
| 25. #4458 | C22 | semidirect |
| 27. #2246 | D3 | semidirect |
| 69. #493 | C2×D3 | semidirect |
| 78. C4×C16 | C2×D3 | semidirect |
| 117. D24 | D8 | semidirect |
| 180. D12 | D16 | semidirect |
| 317. C3 | #12316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81789 | 2 |
| C3×#2246 | 2 |
| #71293 | 2 |
| #71282 | 2 |
| #67790 | 2 |
| #67504 | 2 |
| #67503 | 2 |
| #12316 | 3 |