Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
753 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 753 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #92258 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini | C2×C32 | C2×C32×D3 |
| Fitting, prime radical | C22×C32⋊H(3,𝔽3) | C2 |
| socle | C22×C32 | C32×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. #11757562 | C2 | direct (N × H) |
| 4. C2×C3⋊((C3⋊Dic3)⋊C3) | C3 | semidirect |
| 5. C2×C32⋊H(3,𝔽3) | C4 | semidirect |
| 11. C3⋊((C3⋊Dic3)⋊C3) | C2×C3 | semidirect |
| 12. C32⋊H(3,𝔽3) | C2×C4 | semidirect |
| 13. C2×C3⋊(C3⋊Dic3) | C32 | semidirect |
| 17. C2×C34 | Dic3 | semidirect |
| 21. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 28. C3⋊(C3⋊Dic3) | C2×C32 | semidirect |
| 36. C34 | C2×Dic3 | semidirect |
| 38. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 51. C2×C33 | C32×C4 | semidirect |
| 82. C33 | C2×C32×C4 | semidirect |
| 108. C2×C32 | (C3⋊Dic3)⋊C3 | semidirect |
| 129. C32 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 149. C2 | #11757562 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32⋊H(3,𝔽3) | 2 |
| #11757562 | 2 |
| C2×C32×C3⋊Dic3 | 3 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |