Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #71815 | C2 | semidirect |
| 3. #71802 | C2 | semidirect |
| 4. #69750 | C2 | semidirect |
| 5. #69731 | C2 | semidirect |
| 8. C3×#500 | C4 | semidirect |
| 9. C3×#493 | C4 | semidirect |
| 10. C3×#486 | C4 | semidirect |
| 53. #500 | Dic3 | semidirect |
| 54. #493 | Dic3 | semidirect |
| 55. #486 | Dic3 | semidirect |
| 93. C4×Dic3 | D8 | semidirect |
| 247. C3 | #9847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3169 | 2 |
| #71815 | 2 |
| #71802 | 2 |
| #69750 | 2 |
| #69731 | 2 |
| #9847 | 3 |