Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
600 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C32 | C3×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C32×C22⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C32⋊(C22⋊C9) | C2 | semidirect |
| 3. C3⋊(C3⋊((C22⋊C9)⋊C2)) | C3 | semidirect |
| 10. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. C32⋊(C22⋊C9) | D3 | semidirect |
| 29. C22×C33 | D9 | semidirect |
| 45. C3×C22⋊C9 | C3×D3 | semidirect |
| 87. C22×C32 | C3⋊D9 | semidirect |
| 111. C33 | (C22⋊C9)⋊C2 | semidirect |
| 153. C22×C3 | #4169 | semidirect |
| 177. C32 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 197. C22 | C3⋊#4169 | semidirect |
| 202. C3 | #10619746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C22⋊C9) | 2 |
| C3×#6312 | 3 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 3 |
| #10619746 | 3 |
| C3⋊#4169 | 4 |