Finite Group DatabasebetaFinite Group Databasebeta← C3×C3⋊((C3⋊S4)⋊C3) #14519211
Order 1944.
862 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 862 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, hypercenter | C3 | C3⋊((C3⋊S4)⋊C3) |
| commutator, cosocle, hypocenter | C32×A4 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C3×C3⋊(C3⋊S4) | C3 | semidirect |
| 4. C3⋊((C3⋊S4)⋊C3) | C3 | direct (N × H) |
| 7. C22×C34 | D3 | semidirect |
| 10. C33×A4 | C2×C3 | semidirect |
| 15. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 16. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 18. C3⋊(C3⋊S4) | C32 | semidirect |
| 36. C22×C33 | C3×D3 | semidirect |
| 37. C22×C33 | C3⋊D3 | semidirect |
| 51. C32×A4 | C3×D3 | semidirect |
| 52. C32×A4 | C2×C32 | semidirect |
| 60. C22⋊H(3,𝔽3) | C3×D3 | semidirect |
| 63. C34 | S4 | semidirect |
| 104. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 107. C22×C32 | C3×C3⋊D3 | semidirect |
| 124. C3×A4 | C32×D3 | semidirect |
| 147. C33 | C3×S4 | semidirect |
| 148. C33 | C3⋊S4 | semidirect |
| 189. C22×C3 | C3×(C3⋊D3)⋊C3 | semidirect |
| 190. C22×C3 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 222. C32 | (C3⋊S4)⋊C3 | semidirect |
| 225. C32 | C3×C3⋊S4 | semidirect |
| 241. C22 | C3×C3⋊((C3⋊D3)⋊C3) | semidirect |
| 250. C3 | C3×(C3⋊S4)⋊C3 | semidirect |
| 251. C3 | C3⋊((C3⋊S4)⋊C3) | direct (N × H) |
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 |
| C3×C3⋊(C3⋊S4) | 3 |
| C32×#638 | 3 |
| C3⋊((C3⋊S4)⋊C3) | 3 |
| C3×(C3⋊S4)⋊C3 | 3 |
| C3×C3⋊((C3⋊D3)⋊C3) | 4 |