Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #69298 | C2 | semidirect |
| 3. #68073 | C2 | semidirect |
| 4. C3×#1336 | C2 | semidirect |
| 5. #67766 | C2 | semidirect |
| 6. #67568 | C2 | semidirect |
| 7. #67443 | C2 | semidirect |
| 21. C3×#364 | C22 | semidirect |
| 22. C3×#322 | C22 | semidirect |
| 25. #4463 | C22 | semidirect |
| 27. C8×C3⋊C8 | C22 | semidirect |
| 32. #1336 | D3 | semidirect |
| 85. #364 | C2×D3 | semidirect |
| 89. #322 | C2×D3 | semidirect |
| 325. C3 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79889 | 2 |
| #69298 | 2 |
| #68073 | 2 |
| C3×#1336 | 2 |
| #67766 | 2 |
| #67568 | 2 |
| #67443 | 2 |
| #11670 | 3 |