Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
697 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 697 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C3⋊#1084 | C2 | semidirect |
| 3. C2×C3×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. #10619883 | C2 | direct (N × H) |
| 9. C2×C3⋊((C3⋊D3)⋊C3) | C4 | semidirect |
| 11. C3⋊#1084 | C22 | semidirect |
| 12. C3×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 18. C2×C3×C3⋊Dic3 | D3 | semidirect |
| 25. C2×(C3⋊Dic3)⋊C3 | D3 | semidirect |
| 27. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 29. C3⋊((C3⋊D3)⋊C3) | C2×C4 | semidirect |
| 38. C2×C3⋊(C3⋊D3) | Dic3 | semidirect |
| 45. C3×C3⋊Dic3 | C2×D3 | semidirect |
| 53. (C3⋊Dic3)⋊C3 | C2×D3 | semidirect |
| 54. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 66. C2×C3⋊Dic3 | C3⋊D3 | semidirect |
| 82. C2×C33 | C4×D3 | semidirect |
| 83. C2×C33 | C2×Dic3 | semidirect |
| 86. C3⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 90. C2×H(3,𝔽3) | C4×D3 | semidirect |
| 126. C3⋊Dic3 | C2×C3⋊D3 | semidirect |
| 136. C33 | C2×C4×D3 | semidirect |
| 137. C33 | C22×Dic3 | semidirect |
| 139. H(3,𝔽3) | C2×C4×D3 | semidirect |
| 176. C2×C32 | D3×Dic3 | semidirect |
| 177. C2×C32 | C4×C3⋊D3 | semidirect |
| 225. C32 | C2×D3×Dic3 | semidirect |
| 226. C32 | C2×C4×C3⋊D3 | semidirect |
| 242. C2×C3 | ((C3⋊D3)⋊C3)⋊C4 | semidirect |
| 260. C3 | C2×((C3⋊D3)⋊C3)⋊C4 | semidirect |
| 263. C2 | #10619883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊((C3⋊D3)⋊C3) | 2 |
| C2×C3⋊#1084 | 2 |
| C2×C3×(C3⋊Dic3)⋊C3 | 2 |
| #10619883 | 2 |
| C2×#6294 | 3 |
| C2×#6289 | 3 |
| C2×((C3⋊D3)⋊C3)⋊C4 | 3 |