Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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. C3×#2145 | C2 | semidirect |
| 3. #72081 | C2 | semidirect |
| 4. #71442 | C2 | semidirect |
| 5. #70663 | C2 | semidirect |
| 6. #70656 | C2 | semidirect |
| 7. #67811 | C2 | semidirect |
| 34. #2145 | D3 | semidirect |
| 74. C3×#106 | D4 | semidirect |
| 203. #106 | #67 | semidirect |
| 376. C3 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83904 | 2 |
| C3×#2145 | 2 |
| #72081 | 2 |
| #71442 | 2 |
| #70663 | 2 |
| #70656 | 2 |
| #67811 | 2 |
| #13416 | 3 |