Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#4517 | C2 | semidirect |
| 5. #70710 | C2 | semidirect |
| 6. #67813 | C2 | semidirect |
| 7. #67733 | C2 | semidirect |
| 18. #5195 | C4 | semidirect |
| 327. C3 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83910 | 2 |
| C2×#5195 | 2 |
| C3×#2148 | 2 |
| C2×#4517 | 2 |
| #70710 | 2 |
| #67813 | 2 |
| #67733 | 2 |
| #13031 | 3 |