Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #73669 | C2 | semidirect |
| 5. #67746 | C2 | semidirect |
| 6. #67737 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 37. C3×C4⋊Q8 | Q8 | semidirect |
| 38. C3×#127 | Q8 | semidirect |
| 149. C4⋊Q8 | Dic6 | semidirect |
| 150. #127 | Dic6 | semidirect |
| 384. C3 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #73669 | 2 |
| C3×#1502 | 2 |
| #71816 | 2 |
| #71811 | 2 |
| #67746 | 2 |
| #67737 | 2 |
| #67620 | 2 |
| #10370 | 3 |