Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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. #67482 | C2 | direct (N × H) |
| 9. C22×Dic12 | C4 | semidirect |
| 12. #5137 | C4 | semidirect |
| 14. C2×#817 | C4 | semidirect |
| 52. C2×Dic12 | C2×C4 | semidirect |
| 54. #817 | C2×C4 | semidirect |
| 305. C2×C3 | #1340 | semidirect |
| 326. C3 | C2×#1340 | semidirect |
| 331. C2 | #67482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5137 | 2 |
| C2×C3×H(3,ℤ/4) | 2 |
| C2×#4553 | 2 |
| #67482 | 2 |
| C2×#1340 | 3 |