Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 93 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. #71450 | C2 | semidirect |
| 3. #71442 | C2 | semidirect |
| 4. #69844 | C2 | semidirect |
| 5. C3×#1375 | C2 | semidirect |
| 25. #1375 | D3 | semidirect |
| 55. #817 | D4 | semidirect |
| 259. C3 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78499 | 2 |
| #71450 | 2 |
| #71442 | 2 |
| #69844 | 2 |
| C3×#1375 | 2 |
| #13416 | 3 |