Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
699 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 699 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⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 2. C2×C3×#1084 | C2 | semidirect |
| 3. #10619902 | C2 | direct (N × H) |
| 8. C2×C3⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 9. C3×#1084 | C22 | semidirect |
| 10. C22×C3⋊(C3⋊D3) | D3 | semidirect |
| 17. C2×#1084 | D3 | semidirect |
| 19. C2×C3×H(3,𝔽3) | D4 | semidirect |
| 28. C2×C3⋊(C3⋊D3) | C2×D3 | semidirect |
| 40. #1084 | C2×D3 | semidirect |
| 41. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 58. C2×C33 | #67 | semidirect |
| 66. C2×H(3,𝔽3) | D12 | semidirect |
| 98. C33 | C2×#67 | semidirect |
| 101. H(3,𝔽3) | C2×D12 | semidirect |
| 125. C2×C32 | #626 | semidirect |
| 161. C32 | C2×#626 | semidirect |
| 174. C2×C3 | #6198 | semidirect |
| 190. C3 | C2×#6198 | semidirect |
| 193. C2 | #10619902 | 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 |
| #10619902 | 2 |
| C2×#6292 | 3 |
| C2×#6198 | 3 |