Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 103 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×#2163 | C2 | semidirect |
| 3. #69732 | C2 | semidirect |
| 4. #67516 | C2 | semidirect |
| 18. C3×#346 | C22 | semidirect |
| 20. #4457 | C22 | semidirect |
| 22. #2163 | D3 | semidirect |
| 63. #346 | C2×D3 | semidirect |
| 245. C3 | #11667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D24 | 2 |
| C3×#2163 | 2 |
| #69732 | 2 |
| #67516 | 2 |
| #11667 | 3 |