Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
508 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 150 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. C3×Q8×H(3,𝔽3) | C2 | semidirect |
| 2. C3×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C3×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. C3×#3832 | C3 | semidirect |
| 6. #88722 | C3 | direct (N × H) |
| 11. C33×Q8 | D3 | semidirect |
| 12. C33×Q8 | C2×C3 | semidirect |
| 13. C3×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 14. C3×C4×C3⋊D3 | C2×C3 | semidirect |
| 18. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 19. C4⋊((C3⋊D3)⋊C3) | C2×C3 | semidirect |
| 20. C4×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 24. #3832 | C32 | semidirect |
| 39. C3×H(3,𝔽3) | #41 | semidirect |
| 49. C32×Q8 | C3×D3 | semidirect |
| 50. C32×Q8 | C2×C32 | semidirect |
| 53. C4⋊(C3⋊D3) | C2×C32 | semidirect |
| 54. C4×C3⋊D3 | C2×C32 | semidirect |
| 95. C33 | #239 | semidirect |
| 96. C33 | C3×#41 | semidirect |
| 98. H(3,𝔽3) | C3×#41 | semidirect |
| 104. C3×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 155. C32 | C3×#239 | semidirect |
| 156. C32 | C32×#41 | semidirect |
| 157. Q8 | C3×(C3⋊D3)⋊C3 | semidirect |
| 179. C3 | #88722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 2 |
| C3×C4⋊((C3⋊D3)⋊C3) | 2 |
| C3×C4×(C3⋊D3)⋊C3 | 2 |
| C3×#3832 | 3 |
| C32×#239 | 3 |
| #88722 | 3 |