Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 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. #79279 | C2 | semidirect |
| 3. C3×#1517 | C2 | semidirect |
| 4. #71798 | C2 | semidirect |
| 5. #69544 | C2 | semidirect |
| 6. #67742 | C2 | semidirect |
| 7. #67630 | C2 | semidirect |
| 13. #5089 | C4 | semidirect |
| 14. #5081 | C4 | semidirect |
| 15. #5074 | C4 | semidirect |
| 16. #5071 | C4 | semidirect |
| 39. #1517 | D3 | semidirect |
| 409. C3 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83293 | 2 |
| #79279 | 2 |
| C3×#1517 | 2 |
| #71798 | 2 |
| #69544 | 2 |
| #67742 | 2 |
| #67630 | 2 |
| #9432 | 3 |