Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1315 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1315 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊(C3⋊(C3⋊S4)) |
| commutator, cosocle, hypocenter | C22⋊H(5,𝔽3) | C2 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C3 | C3⋊(C3⋊(C3⋊D3)) |
| LCS | G ▷ C22⋊H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22⋊H(5,𝔽3) | C2 | semidirect |
| 6. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 8. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 9. A4×H(3,𝔽3) | D3 | semidirect |
| 21. C22×C33 | C3⋊D3 | semidirect |
| 23. C32×A4 | C3⋊D3 | semidirect |
| 25. C22×H(3,𝔽3) | C3⋊D3 | semidirect |
| 27. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 28. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 32. C3×H(3,𝔽3) | S4 | semidirect |
| 57. C33 | C3⋊S4 | semidirect |
| 60. H(3,𝔽3) | C3⋊S4 | semidirect |
| 99. C22 | #92404 | 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 |
| C3⋊#6258 | 3 |
| A4⋊#272 | 3 |
| #10619994 | 3 |
| #92404 | 4 |