Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. C9×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C4×C9×C3⋊D3 | C3 | semidirect |
| 7. C4×(C3⋊D3)⋊C9 | C3 | semidirect |
| 9. C9×(C3⋊D3)⋊C3 | C4 | direct (N × H) |
| 15. C32×C4×C9 | D3 | semidirect |
| 16. C32×C4×C9 | C2×C3 | semidirect |
| 17. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 23. C4×C32⋊C9 | C2×C3 | semidirect |
| 24. (C3⋊Dic3)⋊C9 | C2×C3 | semidirect |
| 25. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 29. C4×(C3⋊D3)⋊C3 | C9 | direct (N × H) |
| 37. C9×C3⋊D3 | C3×C4 | semidirect |
| 43. (C3⋊D3)⋊C9 | C3×C4 | semidirect |
| 57. C4×H(3,𝔽3) | C2×C9 | semidirect |
| 69. (C3⋊Dic3)⋊C3 | C2×C9 | semidirect |
| 75. C32×C9 | C4×D3 | semidirect |
| 76. C32×C9 | C2×C3×C4 | semidirect |
| 79. C32⋊C9 | C2×C3×C4 | semidirect |
| 81. C4×C3⋊D3 | C3×C9 | semidirect |
| 105. (C3⋊D3)⋊C3 | C4×C9 | direct (N × H) |
| 123. C32×C4 | D3×C9 | semidirect |
| 124. C32×C4 | C2×C3×C9 | semidirect |
| 126. C3⋊Dic3 | C2×C3×C9 | semidirect |
| 138. C4×C9 | (C3⋊D3)⋊C3 | direct (N × H) |
| 143. H(3,𝔽3) | C2×C4×C9 | semidirect |
| 170. C3⋊D3 | C3×C4×C9 | semidirect |
| 204. C32 | C4×D3×C9 | semidirect |
| 205. C32 | C2×C3×C4×C9 | semidirect |
| 211. C9 | C4×(C3⋊D3)⋊C3 | direct (N × H) |
| 226. C4 | C9×(C3⋊D3)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×(C3⋊D3)⋊C3 | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| C9×(C3⋊Dic3)⋊C3 | 2 |
| C4×C9×C3⋊D3 | 3 |
| C3×C4×(C3⋊D3)⋊C3 | 3 |
| C3×C4×D3×C9 | 3 |
| C4×(C3⋊D3)⋊C9 | 3 |