Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1013 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1013 conjugacy classes of subgroups — too many to draw. Only its 203 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 | #92391 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini | C2×C3 | C2×C32×C3⋊D3 |
| Fitting, prime radical | C22×H(5,𝔽3) | C2 |
| socle | C22×C3 | C32×C3⋊D3 |
| cosocle | C2×C33 | C22×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11758012 | C2 | direct (N × H) |
| 3. C2×C3⋊((C3⋊Dic3)⋊C3) | C3 | semidirect |
| 5. C2×H(5,𝔽3) | C4 | semidirect |
| 11. C3⋊((C3⋊Dic3)⋊C3) | C2×C3 | semidirect |
| 13. H(5,𝔽3) | C2×C4 | semidirect |
| 14. C2×C3⋊(C3⋊Dic3) | C32 | semidirect |
| 22. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 23. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 33. C3⋊(C3⋊Dic3) | C2×C32 | semidirect |
| 45. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 46. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 60. C2×C33 | C3×Dic3 | semidirect |
| 61. C2×C33 | C3⋊Dic3 | semidirect |
| 62. C2×C33 | C32×C4 | semidirect |
| 76. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 98. C33 | C2×C3×Dic3 | semidirect |
| 99. C33 | C2×C3⋊Dic3 | semidirect |
| 100. C33 | C2×C32×C4 | semidirect |
| 106. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 169. C2 | #11758012 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(5,𝔽3) | 2 |
| #11758012 | 2 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |