Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
482 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 127 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×#2150 | C2 | semidirect |
| 3. C2×#4517 | C2 | semidirect |
| 5. C4×#819 | C2 | semidirect |
| 22. #2150 | D3 | semidirect |
| 242. C3 | #13258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4696 | 2 |
| C3×#2150 | 2 |
| C2×#4517 | 2 |
| C2×#4516 | 2 |
| C4×#819 | 2 |
| #13258 | 3 |