Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
946 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 946 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. #83843 | C2 | semidirect |
| 3. #72052 | C2 | semidirect |
| 4. #71784 | C2 | semidirect |
| 6. #69779 | C2 | semidirect |
| 13. C3×#492 | C4 | semidirect |
| 37. C2×C3×SD16 | C2×C4 | semidirect |
| 40. C3×C4⋊Q8 | C2×C4 | semidirect |
| 51. C3×C4×C8 | C2×C4 | semidirect |
| 57. #818 | D4 | semidirect |
| 58. #817 | D4 | semidirect |
| 66. #492 | Dic3 | semidirect |
| 117. C2×SD16 | C2×Dic3 | semidirect |
| 121. C4⋊Q8 | C2×Dic3 | semidirect |
| 140. C4×C8 | C2×Dic3 | semidirect |
| 253. C3 | #23198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#492 | 2 |
| #83843 | 2 |
| #72052 | 2 |
| #71784 | 2 |
| #71763 | 2 |
| #69779 | 2 |
| #23198 | 3 |