Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
864 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C3⋊D3×C3⋊D9 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊D32 |
| 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 |
|---|---|---|
| 19. C33×C9 | Q8 | semidirect |
| 54. C32×C9 | Dic6 | semidirect |
| 55. C32×C9 | Dic6 | semidirect |
| 95. C33 | Dic18 | semidirect |
| 102. C3×C9 | #627 | semidirect |
| 103. C3×C9 | #634 | semidirect |
| 134. C32 | #6189 | semidirect |
| 135. C32 | #6226 | semidirect |
| 139. C9 | #6293 | semidirect |
| 151. C3 | #10619867 | semidirect |
| 152. C3 | #10619868 | 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 |
| C32×C3⋊Dic9 | 2 |
| #10620153 | 3 |
| #10619868 | 3 |
| #10619867 | 3 |