Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 13. C3×#125 | C8 | semidirect |
| 50. #125 | C3⋊C8 | semidirect |
| 135. C3 | #7134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1994 | 2 |
| #67611 | 2 |
| #7134 | 3 |