Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. C2×#4680 | C2 | semidirect |
| 5. #70522 | C2 | semidirect |
| 6. #70507 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 333. C3 | #10166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83283 | 2 |
| #83270 | 2 |
| C2×#4680 | 2 |
| C3×#1492 | 2 |
| #70522 | 2 |
| #70507 | 2 |
| #67656 | 2 |
| #10166 | 3 |