Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
630 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. C3×#2972 | C2 | semidirect |
| 3. #71601 | C2 | semidirect |
| 4. #70757 | C2 | semidirect |
| 5. #67737 | C2 | semidirect |
| 22. #2972 | D3 | semidirect |
| 40. #940 | C8 | semidirect |
| 51. C3×C4×C8 | D4 | semidirect |
| 95. C2×D12 | C2×C8 | semidirect |
| 111. C4×Dic3 | C2×C8 | semidirect |
| 140. C4×C8 | #67 | semidirect |
| 319. C3 | #9101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2972 | 2 |
| #82329 | 2 |
| #71601 | 2 |
| #70757 | 2 |
| #67737 | 2 |
| #9101 | 3 |