Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
723 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 723 conjugacy classes of subgroups — too many to draw. Only its 83 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×#272 | C2 | semidirect |
| 2. C22×C3⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C2×C3⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 4. #10619904 | C2 | direct (N × H) |
| 10. C2×C3×#272 | C22 | semidirect |
| 12. C2×C3⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 13. C3⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 14. C22×C3⋊(C3⋊D3) | D3 | semidirect |
| 19. C2×C3⋊(C3⋊Dic3) | D3 | semidirect |
| 23. C22×#272 | D3 | semidirect |
| 29. C2×C3×H(3,𝔽3) | D4 | semidirect |
| 42. C2×C3⋊(C3⋊D3) | C2×D3 | semidirect |
| 51. C3⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 58. C2×#272 | C2×D3 | semidirect |
| 65. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 92. C2×C33 | D12 | semidirect |
| 93. C2×C33 | #67 | semidirect |
| 107. C2×H(3,𝔽3) | #67 | semidirect |
| 159. C33 | C2×D12 | semidirect |
| 160. C33 | C2×#67 | semidirect |
| 164. H(3,𝔽3) | C2×#67 | semidirect |
| 199. C2×C32 | #625 | semidirect |
| 201. C2×C32 | #626 | semidirect |
| 258. C32 | C2×#625 | semidirect |
| 260. C32 | C2×#626 | semidirect |
| 280. C2×C3 | #6200 | semidirect |
| 303. C3 | C2×#6200 | semidirect |
| 307. C2 | #10619904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#272 | 2 |
| C22×C3⋊((C3⋊D3)⋊C3) | 2 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| #10619904 | 2 |
| C2×#6291 | 3 |
| C2×#6290 | 3 |
| C2×#6200 | 3 |