Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1382 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 2. #78620 | C2 | semidirect |
| 5. #70063 | C2 | semidirect |
| 6. Dic3×#100 | C2 | semidirect |
| 7. #69974 | C2 | semidirect |
| 21. #5118 | C22 | semidirect |
| 22. Dic3×M16 | C22 | semidirect |
| 24. #4554 | C22 | semidirect |
| 279. C3 | #20729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5798 | 2 |
| #78620 | 2 |
| C3×#1783 | 2 |
| #72129 | 2 |
| #70063 | 2 |
| Dic3×#100 | 2 |
| #69974 | 2 |
| #20729 | 3 |