Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
2998 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2998 conjugacy classes of subgroups — too many to draw. Only its 462 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. C2×#13049818 | C2 | direct (N × H) |
| 3. C22×#10620211 | C2 | semidirect |
| 6. C2×#10620211 | C22 | semidirect |
| 8. #13049818 | C22 | direct (N × H) |
| 10. C22×C32×C3⋊D3 | Q8 | semidirect |
| 11. C2×C3⋊D32 | Q8 | semidirect |
| 14. #10620211 | C23 | semidirect |
| 18. C22×C34 | C2×Q8 | semidirect |
| 19. C2×C3⋊(C3⋊(C3⋊D3)) | C2×Q8 | semidirect |
| 21. C2×C32×C3⋊D3 | C2×Q8 | semidirect |
| 22. C3⋊D32 | C2×Q8 | semidirect |
| 35. C2×C34 | C22×Q8 | semidirect |
| 36. C3⋊(C3⋊(C3⋊D3)) | C22×Q8 | semidirect |
| 38. C32×C3⋊D3 | C22×Q8 | semidirect |
| 58. C34 | C23×Q8 | semidirect |
| 68. C22×C3⋊D3 | PSU(3,𝔽2) | semidirect |
| 94. C22×C32 | C2×PSU(3,𝔽2) | semidirect |
| 109. C2×C3⋊D3 | C2×PSU(3,𝔽2) | semidirect |
| 133. C2×C32 | C22×PSU(3,𝔽2) | semidirect |
| 146. C3⋊D3 | C22×PSU(3,𝔽2) | semidirect |
| 168. C32 | C23×PSU(3,𝔽2) | semidirect |
| 189. C22 | #13049818 | direct (N × H) |
| 196. C2 | C2×#13049818 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10620198 | 2 |
| C2×#13049818 | 2 |
| C22×#10620211 | 2 |
| C23×PSU(3,𝔽2) | 9 |