Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
386 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 386 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×D9×H(3,𝔽3) | C2 | semidirect |
| 3. C9⋊#1084 | C2 | semidirect |
| 12. C2×C32×D9 | D3 | semidirect |
| 16. C9×H(3,𝔽3) | D4 | semidirect |
| 33. C2×#272 | D9 | semidirect |
| 44. C32×C9 | #67 | semidirect |
| 79. C2×D9 | #272 | semidirect |
| 84. H(3,𝔽3) | #611 | semidirect |
| 124. C32 | #6194 | semidirect |
| 128. C9 | #6235 | 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×D9×H(3,𝔽3) | 2 |
| C9⋊#1084 | 2 |
| #10619891 | 3 |
| C3×#6194 | 3 |