Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1134 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C3⋊S4 |
| commutator, cosocle, hypocenter | C22⋊H(3,𝔽3) | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C33 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | semidirect |
| 4. C3×#6258 | C3 | direct (N × H) |
| 6. C22×C34 | D3 | semidirect |
| 8. C33×A4 | D3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 19. #6258 | C32 | direct (N × H) |
| 27. C22×C33 | C3×D3 | semidirect |
| 33. C32×A4 | C3×D3 | semidirect |
| 40. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 42. C34 | S4 | semidirect |
| 68. C22×C32 | #272 | semidirect |
| 69. C22×C32 | C32×D3 | semidirect |
| 76. C3×A4 | C32×D3 | semidirect |
| 86. C33 | C3×S4 | semidirect |
| 113. C22×C3 | C3×#272 | semidirect |
| 128. C32 | #6258 | direct (N × H) |
| 129. C32 | C32×S4 | semidirect |
| 142. C22 | C32×#272 | semidirect |
| 148. C3 | C3×#6258 | 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 |
| C33×S4 | 3 |
| C33×#67 | 3 |
| C3×#6258 | 3 |
| C32×#272 | 4 |