Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
461 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C33 | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C32 | C32×D3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. (C3×A4)⋊H(3,𝔽3) | C2 | semidirect |
| 3. C22×C3⋊((C3⋊D3)⋊C3) | C3 | semidirect |
| 4. C3⋊((C3⋊D3)⋊A4) | C3 | semidirect |
| 6. C33×A4 | D3 | semidirect |
| 7. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 14. C22×C3⋊(C3⋊D3) | C32 | semidirect |
| 25. C3⋊((C3⋊D3)⋊C3) | A4 | semidirect |
| 28. C22×C33 | C2×C32 | semidirect |
| 53. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 67. C3⋊(C3⋊D3) | C3×A4 | semidirect |
| 84. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 108. C3×A4 | (C3⋊D3)⋊C3 | semidirect |
| 117. C33 | C2×C3×A4 | semidirect |
| 189. C32 | (C3⋊D3)⋊A4 | semidirect |
| 209. C22 | #92258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C3×A4)⋊H(3,𝔽3) | 2 |
| C3×A4×C3⋊D3 | 3 |
| C22×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3⋊((C3⋊D3)⋊A4) | 3 |
| #92258 | 4 |