Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 95 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×#1835 | C2 | semidirect |
| 3. #69745 | C2 | semidirect |
| 4. #67485 | C2 | semidirect |
| 11. #4695 | C4 | semidirect |
| 14. C4×D24 | C4 | semidirect |
| 15. #4682 | C4 | semidirect |
| 23. #1835 | D3 | semidirect |
| 241. C3 | #11858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78470 | 2 |
| C3×#1835 | 2 |
| #69745 | 2 |
| #67485 | 2 |
| #11858 | 3 |