Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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. #83780 | C2 | semidirect |
| 3. C3×#2115 | C2 | semidirect |
| 4. #71437 | C2 | semidirect |
| 5. #67810 | C2 | semidirect |
| 25. #2115 | D3 | semidirect |
| 58. #812 | D4 | semidirect |
| 279. C3 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83786 | 2 |
| #83780 | 2 |
| C3×#2115 | 2 |
| #71437 | 2 |
| #67810 | 2 |
| #12982 | 3 |