Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
927 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 927 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C2×#14550487 | C2 | semidirect |
| 4. #72221822 | C2 | direct (N × H) |
| 8. #14550487 | C22 | semidirect |
| 15. C2×C3×#6875 | D3 | semidirect |
| 16. C2×C3×#6875 | D3 | semidirect |
| 17. C2×C3×#6875 | D3 | semidirect |
| 34. C2×#6869⋊C2 | C9 | semidirect |
| 45. C3×#6875 | C2×D3 | semidirect |
| 46. C3×#6875 | C2×D3 | semidirect |
| 47. C3×#6875 | C2×D3 | semidirect |
| 98. C2×#6869 | C2×C9 | semidirect |
| 99. #6869⋊C2 | C2×C9 | semidirect |
| 179. #6869 | C22×C9 | semidirect |
| 242. C2×C27⋊C3 | D3×C9 | semidirect |
| 243. C2×C27⋊C3 | D3×C9 | semidirect |
| 244. C2×C27⋊C3 | D3×C9 | semidirect |
| 377. C27⋊C3 | C2×D3×C9 | semidirect |
| 378. C27⋊C3 | C2×D3×C9 | semidirect |
| 379. C27⋊C3 | C2×D3×C9 | semidirect |
| 788. C2 | #72221822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(D9⋊C9) | 3 |
| C2×C3×#6869⋊C2 | 3 |
| C2×#14550487 | 2 |
| #72221822 | 2 |
| C2×C3×AGL(1,ℤ/27) | 3 |