Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
233 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 233 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #4207 |
| commutator, hypocenter | C32⋊C9 | C2×C3×C4 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×#6896 | C2 |
| prime radical | C2×#4181 | C2×C3 |
| cosocle | C2×C32⋊C9 | C22×C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6896 | C2 | semidirect |
| 3. #11757612 | C2 | semidirect |
| 9. #92308 | C4 | direct (N × H) |
| 17. C4×C9⋊C9 | D3 | semidirect |
| 20. C4×C92 | D3 | semidirect |
| 25. #6896 | C2×C4 | semidirect |
| 60. C9⋊C9 | C4×D3 | semidirect |
| 63. C92 | C4×D3 | semidirect |
| 161. C4 | #92308 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92308 | 2 |
| C4×#6896 | 2 |
| #11757612 | 2 |
| C4×#4181 | 3 |
| C4×D9⋊C9 | 3 |
| C4×(C3⋊D3)⋊C9 | 3 |
| C4×C9×D9 | 3 |