Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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. #78545 | C2 | semidirect |
| 5. C3×#1378 | C2 | semidirect |
| 6. #67819 | C2 | semidirect |
| 7. #67818 | C2 | semidirect |
| 32. #1378 | D3 | semidirect |
| 40. C2×Dic12 | Q8 | semidirect |
| 45. C2×D24 | Q8 | semidirect |
| 307. C3 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78545 | 2 |
| #71450 | 2 |
| C2×#4518 | 2 |
| #69897 | 2 |
| C3×#1378 | 2 |
| #67819 | 2 |
| #67818 | 2 |
| #13374 | 3 |