Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 115 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×#4496 | C2 | semidirect |
| 5. #69904 | C2 | semidirect |
| 6. #67734 | C2 | semidirect |
| 7. #67672 | 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 |
|---|---|
| C3×#2957 | 2 |
| C2×#5195 | 2 |
| #72081 | 2 |
| C2×#4496 | 2 |
| #69904 | 2 |
| #67734 | 2 |
| #67672 | 2 |
| #13031 | 3 |