Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
240 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 37 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. #11757762 | C2 | semidirect |
| 3. C22×C9⋊D9 | C3 | semidirect |
| 7. C22×C92 | C2×C3 | semidirect |
| 21. C9⋊D9 | A4 | semidirect |
| 37. C92 | C2×A4 | semidirect |
| 108. C22 | #6899⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757762 | 2 |
| C3⋊(D9⋊A4) | 3 |
| C22×C9⋊D9 | 3 |
| #10619770 | 3 |
| #6899⋊C2 | 4 |