Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
745 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 745 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 1. C22×C3×C32⋊C9 | C2 | semidirect |
| 2. C2×C3⋊#4169 | C2 | semidirect |
| 3. C3⋊#66316 | C2 | semidirect |
| 5. #10619992 | C3 | semidirect |
| 14. C22×C32×C9 | C2×C3 | semidirect |
| 15. C2×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 16. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 18. C22×C32⋊C9 | D3 | semidirect |
| 21. C3×C32⋊C9 | D4 | semidirect |
| 46. C22×C33 | D9 | semidirect |
| 62. C22×C3×C9 | C3×D3 | semidirect |
| 69. C32×C9 | C3×D4 | semidirect |
| 71. C32⋊C9 | #67 | semidirect |
| 121. C22×C32 | C3⋊D9 | semidirect |
| 147. C33 | #611 | semidirect |
| 153. C3×C9 | C3×#67 | semidirect |
| 202. C22×C3 | #4169 | semidirect |
| 226. C32 | #6233 | semidirect |
| 251. C22 | C3⋊#4169 | semidirect |
| 256. C3 | #10619630 | semidirect |
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 |
| C3⋊#66316 | 2 |
| C3×#6312 | 3 |
| #10619992 | 3 |
| #10619630 | 3 |