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. #67821 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 13. C3×#510 | C4 | semidirect |
| 80. #510 | Dic3 | semidirect |
| 327. C3 | #13031 | 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 |
| #72081 | 2 |
| #72069 | 2 |
| C2×#4565 | 2 |
| #67821 | 2 |
| #67814 | 2 |
| #13031 | 3 |