Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
276 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 18. C3×#367 | C4 | semidirect |
| 19. C3×#366 | C4 | semidirect |
| 65. #367 | Dic3 | semidirect |
| 66. #366 | Dic3 | semidirect |
| 235. C3 | #13119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2159 | 2 |
| #70663 | 2 |
| #70605 | 2 |
| #67816 | 2 |
| #67811 | 2 |
| #67726 | 2 |
| #67723 | 2 |
| #13119 | 3 |