Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
274 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 16. #4506 | C4 | semidirect |
| 176. C3 | #13172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2108 | 2 |
| C2×#4506 | 2 |
| C2×#4505 | 2 |
| #69894 | 2 |
| #67817 | 2 |
| #13172 | 3 |