Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11757601 | C2 | direct (N × H) |
| 3. C2×C3⋊(C3⋊Dic9) | C3 | semidirect |
| 7. C2×C9×H(3,𝔽3) | C4 | semidirect |
| 13. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 20. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 32. C2×C32×C9 | Dic3 | semidirect |
| 33. C2×C32×C9 | C3×C4 | semidirect |
| 40. C2×C32⋊C9 | Dic3 | semidirect |
| 63. C32×C9 | C2×Dic3 | semidirect |
| 64. C32×C9 | C2×C3×C4 | semidirect |
| 67. C32⋊C9 | C2×Dic3 | semidirect |
| 85. C2×H(3,𝔽3) | Dic9 | semidirect |
| 129. H(3,𝔽3) | C2×Dic9 | semidirect |
| 158. C2×C32 | C3×Dic9 | semidirect |
| 159. C2×C32 | C3⋊Dic9 | semidirect |
| 170. C2×C9 | (C3⋊Dic3)⋊C3 | semidirect |
| 192. C32 | C2×C3×Dic9 | semidirect |
| 193. C32 | C2×C3⋊Dic9 | semidirect |
| 198. C9 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 223. C2 | #11757601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×H(3,𝔽3) | 2 |
| #11757601 | 2 |
| C2×C3⋊(C3⋊Dic9) | 3 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |
| C2×C3×C3⋊Dic9 | 3 |
| C2×#66316 | 3 |