Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2153 | C2 | semidirect |
| 4. #71419 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67671 | C2 | semidirect |
| 26. #2153 | D3 | semidirect |
| 277. C3 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2153 | 2 |
| #71438 | 2 |
| C2×#4515 | 2 |
| #71419 | 2 |
| #69898 | 2 |
| #67813 | 2 |
| #67671 | 2 |
| #13123 | 3 |