Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
628 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 3. C33×Dic9 | C2 | semidirect |
| 5. C3⋊D3×Dic9 | C3 | direct (N × H) |
| 8. C3×C9×C3⋊D3 | C4 | semidirect |
| 15. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 19. C32×Dic9 | D3 | semidirect |
| 20. C32×Dic9 | C2×C3 | semidirect |
| 21. C33×C9 | C2×C4 | semidirect |
| 36. C9×C3⋊D3 | C3×C4 | semidirect |
| 58. C3×Dic9 | C3×D3 | semidirect |
| 59. C3×Dic9 | C3⋊D3 | direct (N × H) |
| 65. C32×C9 | C4×D3 | semidirect |
| 66. C32×C9 | C2×C3×C4 | semidirect |
| 80. C3×C3⋊D3 | Dic9 | direct (N × H) |
| 116. Dic9 | C3×C3⋊D3 | direct (N × H) |
| 121. C33 | C2×Dic9 | semidirect |
| 131. C3×C9 | C3×C4×D3 | semidirect |
| 132. C3×C9 | C4×C3⋊D3 | semidirect |
| 149. C3⋊D3 | C3×Dic9 | direct (N × H) |
| 179. C32 | D3×Dic9 | semidirect |
| 180. C32 | C2×C3×Dic9 | semidirect |
| 186. C9 | C3×C4×C3⋊D3 | semidirect |
| 206. C3 | C3×D3×Dic9 | semidirect |
| 207. C3 | C3⋊D3×Dic9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C3⋊D3 | 2 |
| C3×C3⋊(C3⋊Dic9) | 2 |
| C33×Dic9 | 2 |
| C3×Dic3×C3⋊D3 | 3 |
| C3⋊D3×Dic9 | 3 |
| C3×D3×Dic9 | 3 |