Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
576 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C3⋊S4)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66368 | C2 | semidirect |
| 3. C3×#6258 | C3 | semidirect |
| 4. #10619747 | C3 | direct (N × H) |
| 6. C22×C34 | D3 | semidirect |
| 9. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. #66368 | C2×C3 | semidirect |
| 19. #6258 | C32 | semidirect |
| 29. C22×C33 | C3×D3 | semidirect |
| 40. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 44. C34 | S4 | semidirect |
| 99. C33 | C3×S4 | semidirect |
| 137. C22×C3 | #4174 | semidirect |
| 172. C22 | C3×#4174 | semidirect |
| 179. C3 | #10619747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66368 | 2 |
| C33×#67 | 3 |
| C3×#6258 | 3 |
| #10619747 | 3 |
| C3×#4174 | 4 |