Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
245 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C22⋊C9 | C2×C3 |
| Frattini | C33 | C3×S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×C22⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(3,𝔽3)⋊(C22⋊C9) | C2 | semidirect |
| 2. C3⋊(C3⋊((C22⋊C9)⋊C2)) | C3 | semidirect |
| 7. C32×C22⋊C9 | C2×C3 | semidirect |
| 28. C22×H(3,𝔽3) | D9 | semidirect |
| 100. H(3,𝔽3) | (C22⋊C9)⋊C2 | semidirect |
| 192. C22 | #92180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)⋊(C22⋊C9) | 2 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 3 |
| #10619977 | 3 |
| #92180 | 4 |