Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
354 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 50 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×#92297 | C2 |
| 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. C9×#1084 | C2 | semidirect |
| 3. #11757601 | C2 | semidirect |
| 8. #92297 | C4 | semidirect |
| 12. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 21. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 32. C3⋊(C3⋊D9) | Dic3 | semidirect |
| 53. #1084 | D9 | semidirect |
| 65. C32×C9 | C4×D3 | semidirect |
| 66. C32×C9 | C2×Dic3 | semidirect |
| 137. H(3,𝔽3) | C4×D9 | semidirect |
| 205. C32 | Dic3×D9 | semidirect |
| 206. C32 | (C3⋊D9)⋊C4 | semidirect |
| 211. C9 | ((C3⋊D3)⋊C3)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92297 | 2 |
| C9×#1084 | 2 |
| #11757601 | 2 |
| #10619901 | 3 |
| #10619872 | 3 |
| Dic3×C3⋊D9 | 3 |