Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 123 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×#2108 | C2 | semidirect |
| 3. C2×#4516 | C2 | semidirect |
| 4. C2×#4506 | C2 | semidirect |
| 5. #69903 | C2 | semidirect |
| 17. C2×D48 | C4 | semidirect |
| 25. #2108 | D3 | semidirect |
| 229. C3 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D48 | 2 |
| C3×#2108 | 2 |
| C2×#4516 | 2 |
| C2×#4506 | 2 |
| #69903 | 2 |
| #13245 | 3 |