Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
558 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C9⋊#1113 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊#1113 |
| socle, prime radical | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | Q8 |
| LCS | G ▷ C2×C33×C9 ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. C33×C9 | Q8 | semidirect |
| 56. C32×C9 | Dic6 | semidirect |
| 57. C32×C9 | Dic6 | semidirect |
| 106. C33 | Dic18 | semidirect |
| 118. C3×C9 | #627 | semidirect |
| 119. C3×C9 | #627 | semidirect |
| 164. C32 | #6189 | semidirect |
| 165. C32 | #6226 | semidirect |
| 170. C9 | #6296 | semidirect |
| 187. C3 | #10619868 | semidirect |
| 188. C3 | #10619895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊(C3⋊Dic9) | 2 |
| C3×C9×C3⋊Dic3 | 2 |
| C3⋊#6296 | 3 |
| #10619895 | 3 |
| #10619868 | 3 |