Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
362 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757748 |
| commutator, hypocenter | C9×H(3,𝔽3) | C2×C4 |
| Frattini, socle | C2×C32 | #1113 |
| Fitting, cosocle | C2×C9×H(3,𝔽3) | C22 |
| prime radical | C2×C3×#272 | D3 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11757601 | C2 | semidirect |
| 6. C9×#272 | C4 | semidirect |
| 10. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 14. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 43. C32×C9 | C4×D3 | semidirect |
| 64. #272 | Dic9 | semidirect |
| 89. H(3,𝔽3) | C2×Dic9 | semidirect |
| 137. C32 | D3×Dic9 | semidirect |
| 141. C9 | #6199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#272 | 2 |
| #11757601 | 2 |
| #10619903 | 3 |
| D3×C3⋊Dic9 | 3 |