Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 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 |
|---|---|---|
| 2. #82954 | C2 | semidirect |
| 3. #71818 | C2 | semidirect |
| 4. #71813 | C2 | semidirect |
| 5. #71718 | C2 | semidirect |
| 6. #67752 | C2 | semidirect |
| 7. #67749 | C2 | semidirect |
| 11. C3×#496 | C4 | semidirect |
| 12. C3×#489 | C4 | semidirect |
| 45. C3×C4⋊Q8 | C2×C4 | semidirect |
| 46. C3×#127 | C2×C4 | semidirect |
| 72. C3×#97 | C2×C4 | semidirect |
| 89. #496 | Dic3 | semidirect |
| 90. #489 | Dic3 | semidirect |
| 172. C4⋊Q8 | C2×Dic3 | semidirect |
| 173. #127 | C2×Dic3 | semidirect |
| 204. #97 | C2×Dic3 | semidirect |
| 435. C3 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3213 | 2 |
| #82954 | 2 |
| #71818 | 2 |
| #71813 | 2 |
| #71718 | 2 |
| #67752 | 2 |
| #67749 | 2 |
| #9381 | 3 |