Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
278 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 21. #4490 | C4 | semidirect |
| 22. #4489 | C4 | semidirect |
| 216. C3 | #13170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1945 | 2 |
| C2×#4493 | 2 |
| #70648 | 2 |
| #69794 | 2 |
| C2×#4461 | 2 |
| #67729 | 2 |
| #67724 | 2 |
| #13170 | 3 |