Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
144 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | (C3⋊D3)⋊A4 |
| commutator, hypocenter | C22×H(3,𝔽3) | C2×C9 |
| Frattini | C3×C9 | D3×A4 |
| Fitting, cosocle | C22×#737 | C2×C3 |
| socle | C22×C3 | (C3⋊D3)⋊C9 |
| prime radical | C22×#272 | C9 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757459 | C2 | semidirect |
| 9. C3×C22⋊C27 | D3 | semidirect |
| 108. C22 | #92181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757459 | 2 |
| C22×#4208 | 3 |
| D3×C22⋊C27 | 3 |
| #92181 | 4 |