Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
256 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 22. #4506 | C4 | semidirect |
| 210. C3 | #13175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2110 | 2 |
| #71429 | 2 |
| C2×#4513 | 2 |
| #69901 | 2 |
| #69893 | 2 |
| #67820 | 2 |
| #67816 | 2 |
| #13175 | 3 |