Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
880 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×A4×C3⋊D3 |
| commutator, socle, cosocle | C22×C33 | C2×C32 |
| Fitting | C22×C34 | C2×C3 |
| hypercenter | C32 | A4×C3⋊D3 |
| hypocenter | C22×C32 | C2×H(3,𝔽3) |
| LCS | G ▷ C22×C33 ▷ C22×C32 | |
| UCS | C1 ◁ C3 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C22×C32×C3⋊D3 | C3 | semidirect |
| 3. C3×A4×C3⋊D3 | C3 | semidirect |
| 6. C22×C34 | C2×C3 | semidirect |
| 9. C33×A4 | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 23. C32×C3⋊D3 | A4 | semidirect |
| 28. C22×C33 | C3×D3 | semidirect |
| 39. C32×A4 | C3×D3 | semidirect |
| 43. C22⋊H(3,𝔽3) | C3⋊D3 | direct (N × H) |
| 45. C34 | C2×A4 | semidirect |
| 50. C22×C3⋊D3 | H(3,𝔽3) | semidirect |
| 77. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 79. C22×C32 | C3×C3⋊D3 | semidirect |
| 91. C3×A4 | C3×C3⋊D3 | semidirect |
| 99. C33 | D3×A4 | semidirect |
| 122. C3⋊D3 | C22⋊H(3,𝔽3) | direct (N × H) |
| 135. C22×C3 | D3×H(3,𝔽3) | semidirect |
| 153. C32 | C2×C22⋊H(3,𝔽3) | semidirect |
| 155. C32 | A4×C3⋊D3 | semidirect |
| 171. C22 | C3⋊D3×H(3,𝔽3) | semidirect |
| 177. C3 | D3×C22⋊H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊H(3,𝔽3) | 2 |
| C22×C32×C3⋊D3 | 3 |
| C3×A4×C3⋊D3 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| C3⋊D3×H(3,𝔽3) | 4 |