Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
954 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #4169 |
| commutator, cosocle, hypocenter | C3×C9 | C23×C32 |
| Frattini | C32 | C22×C32×D3 |
| Fitting | C22×C3×C32⋊C9 | C2 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C32⋊C9 | C2 | semidirect |
| 2. C2×C3×#4169 | C2 | direct (N × H) |
| 4. C22×C3×C3⋊D9 | C3 | semidirect |
| 5. C22×#4169 | C3 | direct (N × H) |
| 6. C2×C3×C32⋊C9 | C22 | semidirect |
| 7. C3×#4169 | C22 | direct (N × H) |
| 11. C22×C32×C9 | C2×C3 | semidirect |
| 12. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 14. C22×C32⋊C9 | C2×C3 | semidirect |
| 15. C2×#4169 | C2×C3 | direct (N × H) |
| 16. C3×C32⋊C9 | C23 | semidirect |
| 22. C22×C3⋊D9 | C32 | semidirect |
| 27. C2×C32×C9 | C22×C3 | semidirect |
| 28. C3×C3⋊D9 | C22×C3 | semidirect |
| 30. C2×C32⋊C9 | C22×C3 | semidirect |
| 31. #4169 | C22×C3 | direct (N × H) |
| 38. C22×C33 | D9 | semidirect |
| 52. C22×C3×C9 | C2×C32 | semidirect |
| 53. C2×C3⋊D9 | C2×C32 | semidirect |
| 57. C32×C9 | C23×C3 | semidirect |
| 59. C32⋊C9 | C23×C3 | semidirect |
| 75. C2×C33 | C2×D9 | semidirect |
| 89. C2×C3×C9 | C22×C32 | semidirect |
| 90. C3⋊D9 | C22×C32 | semidirect |
| 106. C22×C32 | C3×D9 | semidirect |
| 127. C33 | C22×D9 | semidirect |
| 136. C3×C9 | C23×C32 | semidirect |
| 156. C2×C32 | C2×C3×D9 | semidirect |
| 178. C22×C3 | #4169 | direct (N × H) |
| 198. C32 | C22×C3×D9 | semidirect |
| 213. C2×C3 | C2×#4169 | direct (N × H) |
| 221. C22 | C3×#4169 | direct (N × H) |
| 227. C3 | C22×#4169 | direct (N × H) |
| 232. C2 | C2×C3×#4169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C32⋊C9 | 2 |
| C2×C3×#4169 | 2 |
| C22×C32×C3⋊D3 | 3 |
| C22×C3×C3⋊D9 | 3 |
| C22×#4169 | 3 |