Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 117 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. #83823 | C2 | semidirect |
| 3. #72086 | C2 | semidirect |
| 4. #72076 | C2 | semidirect |
| 5. #72033 | C2 | semidirect |
| 6. #67818 | C2 | semidirect |
| 7. #67813 | C2 | semidirect |
| 14. C2×C3×SD32 | C4 | semidirect |
| 15. C2×C3×D16 | C4 | semidirect |
| 41. C2×C3×Q16 | C2×C4 | semidirect |
| 47. C2×C3×D8 | C2×C4 | semidirect |
| 62. C2×C3×C16 | C2×C4 | semidirect |
| 80. C2×SD32 | Dic3 | semidirect |
| 81. C2×D16 | Dic3 | semidirect |
| 148. C2×Q16 | C2×Dic3 | semidirect |
| 154. C2×D8 | C2×Dic3 | semidirect |
| 172. C2×C16 | C2×Dic3 | semidirect |
| 340. C3 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#509 | 2 |
| #83823 | 2 |
| #72086 | 2 |
| #72076 | 2 |
| #72033 | 2 |
| #67818 | 2 |
| #67813 | 2 |
| #13033 | 3 |