Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
444 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#92297 |
| commutator, cosocle | C2×C32×C9 | C22×C3 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×C9×H(3,𝔽3) | C2 |
| hypercenter | C4 | #92297 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C2×C32×C9 ▷ C32×C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92297 | C2 | semidirect |
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊D9)) | C3 | semidirect |
| 9. C2×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 14. C32×C4×C9 | D3 | semidirect |
| 15. C32×C4×C9 | C2×C3 | semidirect |
| 19. C4×C32⋊C9 | D3 | semidirect |
| 20. C9×H(3,𝔽3) | D4 | semidirect |
| 50. C4×H(3,𝔽3) | D9 | semidirect |
| 60. C32×C9 | D12 | semidirect |
| 61. C32×C9 | C3×D4 | semidirect |
| 64. C32⋊C9 | D12 | semidirect |
| 108. C32×C4 | C3×D9 | semidirect |
| 109. C32×C4 | C3⋊D9 | semidirect |
| 116. C4×C9 | (C3⋊D3)⋊C3 | semidirect |
| 121. H(3,𝔽3) | D36 | semidirect |
| 178. C32 | C3×D36 | semidirect |
| 179. C32 | C4⋊(C3⋊D9) | semidirect |
| 184. C9 | C4⋊((C3⋊D3)⋊C3) | semidirect |
| 199. C4 | #92297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92297 | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| C4⋊(C3⋊(C3⋊D9)) | 3 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊#4169 | 3 |