Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. C2×#4513 | C2 | semidirect |
| 5. #70700 | C2 | semidirect |
| 6. #67814 | C2 | semidirect |
| 7. #67733 | C2 | semidirect |
| 21. C3×#362 | C4 | semidirect |
| 22. C3×#361 | C4 | semidirect |
| 80. #362 | Dic3 | semidirect |
| 81. #361 | Dic3 | semidirect |
| 283. C3 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83910 | 2 |
| C3×#2148 | 2 |
| C2×#4566 | 2 |
| C2×#4513 | 2 |
| #70700 | 2 |
| #67814 | 2 |
| #67733 | 2 |
| #12952 | 3 |