Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
565 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 58 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 | C3 | C3×A4×C3⋊D3 |
| Fitting | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C3 | C32×C3⋊D3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22⋊H(5,𝔽3) | C2 | semidirect |
| 2. C22×C3⋊((C3⋊D3)⋊C3) | C3 | semidirect |
| 3. C3⋊((C3⋊D3)⋊A4) | C3 | semidirect |
| 7. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 13. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 17. A4×H(3,𝔽3) | D3 | semidirect |
| 19. C22×C3⋊(C3⋊D3) | C32 | semidirect |
| 29. C3⋊((C3⋊D3)⋊C3) | A4 | semidirect |
| 33. C22×C33 | C3×D3 | semidirect |
| 34. C22×C33 | C2×C32 | semidirect |
| 45. C32×A4 | C3×D3 | semidirect |
| 46. C32×A4 | C3⋊D3 | semidirect |
| 48. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 60. C22⋊H(3,𝔽3) | C3×D3 | semidirect |
| 61. C22⋊H(3,𝔽3) | C3×D3 | semidirect |
| 70. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 83. C3⋊(C3⋊D3) | C3×A4 | semidirect |
| 133. C33 | D3×A4 | semidirect |
| 134. C33 | C2×C3×A4 | semidirect |
| 147. H(3,𝔽3) | D3×A4 | semidirect |
| 230. C22 | #92391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊H(5,𝔽3) | 2 |
| C22×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3⋊((C3⋊D3)⋊A4) | 3 |
| C3×(C3⋊D3)⋊A4 | 3 |
| A4×(C3⋊D3)⋊C3 | 3 |
| #92391 | 4 |