Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
558 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213199 |
| commutator, hypocenter | C34 | C2×C4×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C4×C8 |
| prime radical | C2×C3⋊D32 | C2×C4 |
| cosocle | #10620198 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #72213199 | C2 | direct (N × H) |
| 6. C2×#10620193 | C4 | semidirect |
| 7. C2×#10620192 | C4 | semidirect |
| 8. #13049788 | C4 | semidirect |
| 14. C2×C3⋊(C3⋊#157) | C8 | semidirect |
| 15. C2×C32×#157 | C8 | semidirect |
| 19. C3⋊D3×#157 | C8 | semidirect |
| 21. #10620193 | C2×C4 | semidirect |
| 22. #10620192 | C2×C4 | semidirect |
| 32. C3⋊(C3⋊#157) | C2×C8 | semidirect |
| 33. C32×#157 | C2×C8 | semidirect |
| 42. C2×C34 | C4×C8 | semidirect |
| 43. C3⋊(C3⋊(C3⋊D3)) | C4×C8 | semidirect |
| 45. C32×C3⋊D3 | C4×C8 | semidirect |
| 67. C34 | C2×C4×C8 | semidirect |
| 78. C2×#157 | AGL(1,𝔽9) | semidirect |
| 118. #157 | C2×AGL(1,𝔽9) | semidirect |
| 137. C2×C32 | C4×AGL(1,𝔽9) | semidirect |
| 148. C3⋊D3 | C4×AGL(1,𝔽9) | semidirect |
| 174. C32 | C2×C4×AGL(1,𝔽9) | semidirect |
| 211. C2 | #72213199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1572 | 2 |
| C2×#13049788 | 2 |
| #72213199 | 2 |
| C2×C4×AGL(1,𝔽9) | 9 |