Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 231. C3 | #10279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5021 | 2 |
| C2×#4682 | 2 |
| C3×#1984 | 2 |
| C2×#4481 | 2 |
| #67654 | 2 |
| #10279 | 3 |