Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 456 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. #72069 | C2 | semidirect |
| 5. C2×#4565 | C2 | semidirect |
| 6. #67820 | C2 | semidirect |
| 7. #67813 | C2 | semidirect |
| 14. C2×C3×Q32 | C4 | semidirect |
| 15. C2×C3×SD32 | C4 | semidirect |
| 80. C2×Q32 | Dic3 | semidirect |
| 81. C2×SD32 | Dic3 | semidirect |
| 325. C3 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#510 | 2 |
| #83910 | 2 |
| #72080 | 2 |
| #72069 | 2 |
| C2×#4565 | 2 |
| #67820 | 2 |
| #67813 | 2 |
| #13035 | 3 |