Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92297 |
| commutator, hypocenter | C32×C9 | C2×C3×C4 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×C9×H(3,𝔽3) | C2 |
| prime radical | C2×#92297 | C2 |
| cosocle | C2×C32×C9 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. #11757601 | C2 | semidirect |
| 4. C4×C3⋊(C3⋊D9) | C3 | semidirect |
| 9. #92297 | C4 | direct (N × H) |
| 15. C32×C4×C9 | D3 | semidirect |
| 16. C32×C4×C9 | C2×C3 | semidirect |
| 17. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 23. C4×C32⋊C9 | D3 | semidirect |
| 25. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 37. C3⋊(C3⋊D9) | C3×C4 | semidirect |
| 57. C4×H(3,𝔽3) | D9 | semidirect |
| 72. C32×C9 | C4×D3 | semidirect |
| 73. C32×C9 | C2×C3×C4 | semidirect |
| 76. C32⋊C9 | C4×D3 | semidirect |
| 120. C32×C4 | C3×D9 | semidirect |
| 121. C32×C4 | C3⋊D9 | semidirect |
| 135. C4×C9 | (C3⋊D3)⋊C3 | semidirect |
| 142. H(3,𝔽3) | C4×D9 | semidirect |
| 204. C32 | C3×C4×D9 | semidirect |
| 205. C32 | C4×C3⋊D9 | semidirect |
| 210. C9 | C4×(C3⋊D3)⋊C3 | semidirect |
| 226. C4 | #92297 | direct (N × H) |
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 |
| #11757601 | 2 |
| C4×C3⋊(C3⋊D9) | 3 |
| C4×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3×C4×C3⋊D9 | 3 |
| C4×#4169 | 3 |