Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
434 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 54 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 | D9×C3⋊D3 |
| commutator, Fitting, cosocle | C2×C9×H(3,𝔽3) | C22 |
| Frattini, socle | C2×C32 | D3×C3⋊D3 |
| hypocenter | C9×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C9×H(3,𝔽3) ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9⋊#272 | C2 | semidirect |
| 2. C2×C9×#272 | C2 | semidirect |
| 3. H(3,𝔽3)×Dic9 | C2 | semidirect |
| 14. C32×Dic9 | D3 | semidirect |
| 16. C9×H(3,𝔽3) | D4 | semidirect |
| 35. C2×#272 | D9 | semidirect |
| 45. C32×C9 | D12 | semidirect |
| 84. Dic9 | #272 | semidirect |
| 87. H(3,𝔽3) | #611 | semidirect |
| 129. C32 | #6195 | semidirect |
| 133. C9 | C4⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊#272 | 2 |
| C2×C9×#272 | 2 |
| H(3,𝔽3)×Dic9 | 2 |
| #10619893 | 3 |
| C3×#6195 | 3 |