Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
615 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #92258 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini, socle | C2×C32 | C2×C32×D3 |
| Fitting | C4×C32⋊H(3,𝔽3) | C2 |
| prime radical | C2×#92258 | C2 |
| cosocle | C2×C33 | C22×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C32⋊H(3,𝔽3) | C2 | semidirect |
| 3. #11757562 | C2 | semidirect |
| 5. C4×C3⋊((C3⋊D3)⋊C3) | C3 | semidirect |
| 7. #92258 | C4 | direct (N × H) |
| 9. C34×C4 | D3 | semidirect |
| 13. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3⋊((C3⋊Dic3)⋊C3) | C2×C3 | semidirect |
| 15. C32⋊H(3,𝔽3) | C2×C4 | semidirect |
| 16. C4×C3⋊(C3⋊D3) | C32 | semidirect |
| 24. C3⋊((C3⋊D3)⋊C3) | C3×C4 | semidirect |
| 32. C33×C4 | C2×C32 | semidirect |
| 33. C3⋊(C3⋊Dic3) | C2×C32 | semidirect |
| 42. C34 | C4×D3 | semidirect |
| 44. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 55. C3⋊(C3⋊D3) | C32×C4 | semidirect |
| 78. C32×C4 | (C3⋊D3)⋊C3 | semidirect |
| 88. C33 | C2×C32×C4 | semidirect |
| 132. C32 | C4×(C3⋊D3)⋊C3 | semidirect |
| 145. C4 | #92258 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92258 | 2 |
| C4×C32⋊H(3,𝔽3) | 2 |
| #11757562 | 2 |
| C32×C4×C3⋊D3 | 3 |
| C4×C3⋊((C3⋊D3)⋊C3) | 3 |