Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
522 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×C9×C3⋊Dic3 | C2 | semidirect |
| 3. C32×C3⋊Dic9 | C2 | semidirect |
| 5. #10619896 | C3 | direct (N × H) |
| 9. C32×C3⋊D9 | C4 | semidirect |
| 19. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 21. C3×C3⋊Dic9 | D3 | semidirect |
| 22. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 28. C33×C9 | C2×C4 | semidirect |
| 53. C3×C3⋊D9 | Dic3 | semidirect |
| 54. C3×C3⋊D9 | C3×C4 | semidirect |
| 67. C3×C3⋊Dic3 | D9 | semidirect |
| 83. C3⋊Dic9 | C3×D3 | semidirect |
| 108. C32×C9 | C4×D3 | semidirect |
| 109. C32×C9 | C2×Dic3 | semidirect |
| 110. C32×C9 | C2×C3×C4 | semidirect |
| 168. C3⋊D9 | C3×Dic3 | semidirect |
| 189. C3⋊Dic3 | C3×D9 | semidirect |
| 225. C33 | C4×D9 | semidirect |
| 255. C3×C9 | D3×Dic3 | semidirect |
| 256. C3×C9 | C3×C4×D3 | semidirect |
| 257. C3×C9 | C2×C3×Dic3 | semidirect |
| 367. C32 | Dic3×D9 | semidirect |
| 368. C32 | (C3⋊D9)⋊C4 | semidirect |
| 369. C32 | C3×C4×D9 | semidirect |
| 380. C9 | C3×D3×Dic3 | semidirect |
| 417. C3 | C3×Dic3×D9 | semidirect |
| 418. C3 | C3×(C3⋊D9)⋊C4 | semidirect |
| 419. C3 | #10619896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C3⋊D9 | 2 |
| C3×C9×C3⋊Dic3 | 2 |
| C32×C3⋊Dic9 | 2 |
| C3×#6294 | 3 |
| #10619896 | 3 |
| C3×(C3⋊D9)⋊C4 | 3 |
| C3×Dic3×D9 | 3 |