Finite Group DatabasebetaFinite Group DatabasebetaOrder 1584.
168 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D33 |
| commutator | C2×C32×C11 | C2×C4 |
| Fitting, socle, cosocle | C22×C32×C11 | C22 |
| prime radical | C22×C3⋊D33 | C2 |
| hypocenter | C32×C11 | C22⋊C4 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×Dic33 | C2 | semidirect |
| 3. C2×C3×C11×Dic3 | C2 | semidirect |
| 9. C2×C3⋊D33 | C4 | semidirect |
| 16. C2×Dic33 | D3 | semidirect |
| 17. C2×C11×Dic3 | D3 | semidirect |
| 41. C32×C11 | C22⋊C4 | semidirect |
| 47. C2×C3×Dic3 | D11 | semidirect |
| 75. C3×C11 | (C2×D3)⋊C4 | semidirect |
| 76. C3×C11 | (C2×D3)⋊C4 | semidirect |
| 83. C2×Dic3 | D33 | semidirect |
| 109. C11 | #3722 | semidirect |
| 110. C32 | (C2×D11)⋊C4 | semidirect |
| 133. C3 | #10587156 | semidirect |
| 134. C3 | #10587203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊D33 | 2 |
| C2×C3×Dic33 | 2 |
| C2×C3×C11×Dic3 | 2 |
| #10587203 | 3 |
| #10587156 | 3 |
| #3722 | 11 |