Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #73397 | C2 | semidirect |
| 4. C3×#1274 | C2 | semidirect |
| 5. #67746 | C2 | semidirect |
| 24. #1274 | D3 | semidirect |
| 38. #874 | Q8 | semidirect |
| 40. #869 | Q8 | semidirect |
| 275. C3 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #73397 | 2 |
| #70789 | 2 |
| #69440 | 2 |
| C3×#1274 | 2 |
| #67746 | 2 |
| #10370 | 3 |