Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
274 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 47 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, Fitting, cosocle, hypocenter | C22×C92 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C22×C92 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C9⋊A4 | C2 | semidirect |
| 4. C22×C9⋊D9 | C3 | semidirect |
| 9. C22×C92 | C2×C3 | semidirect |
| 27. C9⋊D9 | A4 | semidirect |
| 43. C9⋊A4 | D9 | semidirect |
| 51. C92 | C2×A4 | semidirect |
| 79. C22×C9 | C3×D9 | semidirect |
| 80. C22×C9 | AGL(1,ℤ/9) | semidirect |
| 139. C9 | D9⋊A4 | semidirect |
| 140. C9 | A4×D9 | semidirect |
| 154. C22 | #92299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C9⋊A4 | 2 |
| A4×C3⋊D9 | 3 |
| C3⋊(D9⋊A4) | 3 |
| C22×C9⋊D9 | 3 |
| #10619770 | 3 |
| #92299 | 4 |