Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
249 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C3⋊AGL(1,𝔽9) |
| commutator, Fitting, socle | C2×C34 | C2×C8 |
| prime radical | C2×C32×C3⋊D3 | C2×C4 |
| cosocle | C2×C32×#157 | C22 |
| hypocenter | C34 | C4⋊C8 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. C3×C3⋊(C3⋊Dic3) | C8 | semidirect |
| 23. C33×Dic3 | C8 | semidirect |
| 61. C3⋊(C3⋊Dic3) | C3⋊C8 | semidirect |
| 67. C32×Dic3 | C3⋊C8 | semidirect |
| 70. C34 | C4⋊C8 | semidirect |
| 127. C3×Dic3 | AGL(1,𝔽9) | semidirect |
| 134. C33 | C4⋊(C3⋊C8) | semidirect |
| 135. C33 | Dic3⋊C8 | semidirect |
| 193. Dic3 | C3⋊AGL(1,𝔽9) | semidirect |
| 204. C32 | Dic3⋊(C3⋊C8) | semidirect |
| 205. C32 | C4⋊AGL(1,𝔽9) | semidirect |
| 237. C3 | Dic3⋊AGL(1,𝔽9) | semidirect |
| 238. C3 | C4⋊(C3⋊AGL(1,𝔽9)) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C2×C3×C3⋊AGL(1,𝔽9) | 2 |
| C3×Dic3×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 3 |
| Dic3⋊AGL(1,𝔽9) | 3 |
| Dic3⋊(C3⋊C8) | 9 |