Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1482 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 3. #71894 | C2 | direct (N × H) |
| 27. C23×Dic3 | Q8 | semidirect |
| 73. C22×Dic3 | C2×Q8 | semidirect |
| 202. C2×C3 | #2030 | semidirect |
| 222. C3 | C2×#2030 | semidirect |
| 226. C2 | #71894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#543 | 2 |
| C2×#4943 | 2 |
| #71894 | 2 |
| C2×#4526 | 2 |
| C2×#2030 | 3 |