Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
436 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 436 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×C32×C9 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C22×C32×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C22×C3⋊(C3⋊D9) | C3 | semidirect |
| 7. C22×C32×C9 | C2×C3 | semidirect |
| 12. C3×C9×A4 | D3 | semidirect |
| 15. (C3×A4)⋊C9 | D3 | semidirect |
| 26. C3⋊(C3⋊D9) | A4 | semidirect |
| 45. C22⋊H(3,𝔽3) | D9 | semidirect |
| 53. C32×C9 | C2×A4 | semidirect |
| 83. C22×C32 | C3×D9 | semidirect |
| 99. C3×A4 | C3⋊D9 | semidirect |
| 101. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 170. C32 | A4×D9 | semidirect |
| 175. C9 | (C3⋊D3)⋊A4 | semidirect |
| 192. C22 | #92297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊H(3,𝔽3) | 2 |
| C22×C3⋊(C3⋊D9) | 3 |
| C3⋊((C3⋊D3)⋊A4) | 3 |
| A4×C3⋊D9 | 3 |
| #10619770 | 3 |
| #92297 | 4 |