Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #79178 | C2 | semidirect |
| 3. C3×#2145 | C2 | semidirect |
| 4. C2×#4566 | C2 | semidirect |
| 5. #71438 | C2 | semidirect |
| 6. #67816 | C2 | semidirect |
| 7. #67727 | C2 | semidirect |
| 16. #5192 | C4 | semidirect |
| 18. #5160 | C4 | semidirect |
| 32. #2145 | D3 | semidirect |
| 43. C2×C3×Q16 | C2×C4 | semidirect |
| 45. C2×C3×D8 | C2×C4 | semidirect |
| 76. #819 | C2×C4 | semidirect |
| 172. C2×Q16 | C4×D3 | semidirect |
| 174. C2×D8 | C4×D3 | semidirect |
| 380. C3 | #13005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83928 | 2 |
| #79178 | 2 |
| C3×#2145 | 2 |
| C2×#4566 | 2 |
| #71438 | 2 |
| #67816 | 2 |
| #67727 | 2 |
| #13005 | 3 |