Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
563 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 563 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C23×C3 |
| Frattini | C33 | C22×C3×D3 |
| Fitting | C22×#6856 | C2 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6856 | C2 | semidirect |
| 2. C2×#92159 | C2 | direct (N × H) |
| 3. C22×C3⋊#272 | C3 | semidirect |
| 5. C2×#6856 | C22 | semidirect |
| 6. #92159 | C22 | direct (N × H) |
| 7. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 8. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C2×C3⋊#272 | C2×C3 | semidirect |
| 12. #6856 | C23 | semidirect |
| 18. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 19. C2×C3×H(3,𝔽3) | C22×C3 | semidirect |
| 20. C3⋊#272 | C22×C3 | semidirect |
| 34. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 35. C3×H(3,𝔽3) | C23×C3 | semidirect |
| 137. C22 | #92159 | direct (N × H) |
| 145. C2 | C2×#92159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6856 | 2 |
| C2×#92159 | 2 |
| C22×C3⋊#272 | 3 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |