Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
590 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92180 |
| commutator, cosocle, hypocenter | C32×C9 | C23×C3 |
| Frattini | C33 | C22×C3×D3 |
| Fitting | C22×H(3,𝔽3)⋊C9 | C2 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×H(3,𝔽3)⋊C9 | C2 | semidirect |
| 2. C2×#92180 | C2 | direct (N × H) |
| 3. C22×C3⋊(C3⋊D9) | C3 | semidirect |
| 5. C2×H(3,𝔽3)⋊C9 | C22 | semidirect |
| 6. #92180 | C22 | direct (N × H) |
| 8. C22×C32×C9 | C2×C3 | semidirect |
| 9. C2×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 12. H(3,𝔽3)⋊C9 | C23 | semidirect |
| 20. C2×C32×C9 | C22×C3 | semidirect |
| 21. C3⋊(C3⋊D9) | C22×C3 | semidirect |
| 30. C22×H(3,𝔽3) | D9 | semidirect |
| 39. C32×C9 | C23×C3 | semidirect |
| 58. C2×H(3,𝔽3) | C2×D9 | semidirect |
| 94. H(3,𝔽3) | C22×D9 | semidirect |
| 174. C22 | #92180 | direct (N × H) |
| 184. C2 | C2×#92180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(3,𝔽3)⋊C9 | 2 |
| C2×#92180 | 2 |
| C22×C3⋊(C3⋊D9) | 3 |
| C22×C3⋊((C3⋊D3)⋊C3) | 3 |