Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11758094 |
| commutator, hypocenter | C3×#737 | C2×C4 |
| Frattini | C2×C3 | C3⋊#1113 |
| Fitting, cosocle | C2×C3×#737 | C22 |
| socle | C2×C32 | #1113 |
| prime radical | C2×C3×#272 | D3 |
| LCS | G ▷ C3×#737 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#66409 | C2 | semidirect |
| 7. C3×#4208 | C4 | semidirect |
| 12. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 18. C3×#737 | C2×C4 | semidirect |
| 31. #4208 | Dic3 | semidirect |
| 53. #737 | C2×Dic3 | semidirect |
| 58. C32×C9 | C4×D3 | semidirect |
| 113. C3×C9 | D3×Dic3 | semidirect |
| 170. C3 | #10619908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4208 | 2 |
| C3⋊#66409 | 2 |
| #10619908 | 3 |
| #10619903 | 3 |
| D3×C3⋊Dic9 | 3 |