Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #83027 | C2 | semidirect |
| 4. C2×#4543 | C2 | semidirect |
| 5. #67659 | C2 | semidirect |
| 10. C3×#490 | C4 | semidirect |
| 57. #490 | Dic3 | semidirect |
| 264. C3 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#490 | 2 |
| #83027 | 2 |
| #71765 | 2 |
| C2×#4543 | 2 |
| #67659 | 2 |
| #9002 | 3 |