Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#4513 | C2 | semidirect |
| 5. #69844 | C2 | semidirect |
| 6. C3×#1375 | C2 | semidirect |
| 7. #67819 | C2 | semidirect |
| 24. #4509 | C4 | semidirect |
| 31. #1375 | D3 | semidirect |
| 54. C2×C3×C16 | C2×C4 | semidirect |
| 60. #818 | C2×C4 | semidirect |
| 141. C2×C16 | C4×D3 | semidirect |
| 283. C3 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4711 | 2 |
| C2×#4516 | 2 |
| #71440 | 2 |
| C2×#4513 | 2 |
| #69844 | 2 |
| C3×#1375 | 2 |
| #67819 | 2 |
| #12956 | 3 |