Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1834 | C2 | semidirect |
| 3. #69745 | C2 | semidirect |
| 4. #67486 | C2 | semidirect |
| 13. C4×Dic12 | C4 | semidirect |
| 15. #4696 | C4 | semidirect |
| 16. C4×D24 | C4 | semidirect |
| 18. #4683 | C4 | semidirect |
| 26. #1834 | D3 | semidirect |
| 288. C3 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78469 | 2 |
| C3×#1834 | 2 |
| #69745 | 2 |
| #67486 | 2 |
| #67485 | 2 |
| #11860 | 3 |