Finite Group DatabasebetaFinite Group Databasebeta← C3⋊(C3⋊((C3⋊S4)⋊C3)) #14519226
Order 1944.
1158 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 114 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 | C33×A4 | C2×C3 |
| Frattini | C3 | C3×C3⋊(C3⋊S4) |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C33×A4 | |
| UCS | C1 | |
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 |
| 6. C22×C34 | D3 | semidirect |
| 9. C33×A4 | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 27. C22×C33 | C3⋊D3 | semidirect |
| 34. C32×A4 | C3×D3 | semidirect |
| 39. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 42. C34 | S4 | semidirect |
| 65. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 67. C22×C32 | C3⋊(C3⋊D3) | semidirect |
| 75. C3×A4 | C3×C3⋊D3 | semidirect |
| 87. C33 | C3⋊S4 | semidirect |
| 110. C22×C3 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 126. C32 | (C3⋊S4)⋊C3 | semidirect |
| 128. C32 | C3⋊(C3⋊S4) | semidirect |
| 140. C22 | C3⋊(C3⋊((C3⋊D3)⋊C3)) | semidirect |
| 146. C3 | C3⋊((C3⋊S4)⋊C3) | 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 |
| C3⋊(C3⋊(C3⋊S4)) | 3 |
| C3×#6312 | 3 |
| C3⋊((C3⋊S4)⋊C3) | 3 |
| C3⋊(C3⋊((C3⋊D3)⋊C3)) | 4 |