Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
616 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×A4×C3⋊D3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Fitting | C22×C3×H(3,𝔽3) | C2×C3 |
| socle | C22×C3 | C32×C3⋊D3 |
| hypercenter | C32 | A4×C3⋊D3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C3 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22⋊H(5,𝔽3) | C2 | semidirect |
| 2. C22×C3×#272 | C3 | semidirect |
| 3. A4×#272 | C3 | semidirect |
| 6. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 12. A4×H(3,𝔽3) | C2×C3 | semidirect |
| 16. C22×#272 | C32 | semidirect |
| 21. C3×#272 | A4 | semidirect |
| 23. C22×C33 | C3×D3 | semidirect |
| 27. C32×A4 | C3×D3 | semidirect |
| 41. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 55. #272 | C3×A4 | semidirect |
| 72. C33 | D3×A4 | semidirect |
| 130. C22 | #92392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊H(5,𝔽3) | 2 |
| C22×C3×#272 | 3 |
| A4×#272 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| #92392 | 4 |