Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
612 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C32 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C32 | C22×C32×D3 |
| Fitting | C22×C3×#731 | C2 |
| prime radical | C22×C3×#272 | C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×#731 | C2 | semidirect |
| 2. C2×C3×#4176 | C2 | direct (N × H) |
| 5. C22×#4176 | C3 | direct (N × H) |
| 6. C2×C3×#731 | C22 | semidirect |
| 7. C3×#4176 | C22 | direct (N × H) |
| 10. C22×C32×C9 | D3 | semidirect |
| 14. C22×#731 | C2×C3 | semidirect |
| 15. C2×#4176 | C2×C3 | direct (N × H) |
| 16. C3×#731 | C23 | semidirect |
| 24. C2×C32×C9 | C2×D3 | semidirect |
| 28. C2×#731 | C22×C3 | semidirect |
| 29. #4176 | C22×C3 | direct (N × H) |
| 43. C22×C3×C9 | C3×D3 | semidirect |
| 48. C32×C9 | C22×D3 | semidirect |
| 50. #731 | C23×C3 | semidirect |
| 70. C2×C3×C9 | C2×C3×D3 | semidirect |
| 98. C3×C9 | C22×C3×D3 | semidirect |
| 124. C22×C3 | #4176 | direct (N × H) |
| 144. C2×C3 | C2×#4176 | direct (N × H) |
| 149. C22 | C3×#4176 | direct (N × H) |
| 154. C3 | C22×#4176 | direct (N × H) |
| 157. C2 | C2×C3×#4176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#731 | 2 |
| C2×C3×#4176 | 2 |
| C22×C3×#272 | 3 |
| C22×C3×D3×C9 | 3 |
| C22×#4176 | 3 |