Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#4858 | C2 | semidirect |
| 5. C3×#1383 | C2 | semidirect |
| 6. #67810 | C2 | semidirect |
| 7. #67730 | C2 | semidirect |
| 29. #1383 | D3 | semidirect |
| 287. C3 | #13372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4858 | 2 |
| C2×#4518 | 2 |
| #70696 | 2 |
| C2×#4488 | 2 |
| C3×#1383 | 2 |
| #67810 | 2 |
| #67730 | 2 |
| #13372 | 3 |