Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
615 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 81 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×#92258 |
| commutator, cosocle | C2×C33 | C22×C32 |
| Frattini, socle | C2×C32 | C2×C32×D3 |
| Fitting | C4×C32⋊H(3,𝔽3) | C2 |
| hypercenter | C4 | #92258 |
| hypocenter | C33 | C32×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92258 | C2 | semidirect |
| 2. C4×C32⋊H(3,𝔽3) | C2 | semidirect |
| 4. C4⋊(C3⋊((C3⋊D3)⋊C3)) | C3 | semidirect |
| 8. C34×C4 | D3 | semidirect |
| 9. C2×C3⋊((C3⋊D3)⋊C3) | C2×C3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C32⋊H(3,𝔽3) | D4 | semidirect |
| 13. C4⋊(C3⋊(C3⋊D3)) | C32 | semidirect |
| 22. C2×C3⋊(C3⋊D3) | C2×C32 | semidirect |
| 29. C33×C4 | C2×C32 | semidirect |
| 35. C34 | D12 | semidirect |
| 37. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 70. C32×C4 | (C3⋊D3)⋊C3 | semidirect |
| 76. C33 | C32×D4 | semidirect |
| 117. C32 | C4⋊((C3⋊D3)⋊C3) | semidirect |
| 129. C4 | #92258 | semidirect |
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 |
| C32×C4⋊(C3⋊D3) | 3 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |