Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
924 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 136 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. C2×C3×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 2. C32×#638 | C2 | semidirect |
| 3. C33×#67 | C2 | semidirect |
| 4. C3×#6293 | C2 | semidirect |
| 5. C3×#6290 | C2 | semidirect |
| 6. C3×Dic3×C3⋊D3 | C2 | semidirect |
| 7. C3×D3×C3⋊Dic3 | C2 | semidirect |
| 9. #89029 | C3 | direct (N × H) |
| 19. C2×C3⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 22. C3×#638 | D3 | semidirect |
| 23. C3×#638 | C2×C3 | semidirect |
| 32. C32×#67 | D3 | semidirect |
| 33. C32×#67 | C2×C3 | semidirect |
| 34. #6293 | C2×C3 | semidirect |
| 35. #6290 | C2×C3 | semidirect |
| 36. Dic3×C3⋊D3 | C2×C3 | semidirect |
| 37. D3×C3⋊Dic3 | C2×C3 | semidirect |
| 81. C34 | #41 | semidirect |
| 87. #638 | C3×D3 | semidirect |
| 100. C3×#67 | C3×D3 | semidirect |
| 101. C3×#67 | C3⋊D3 | semidirect |
| 190. C33 | #237 | semidirect |
| 191. C33 | #237 | semidirect |
| 192. C33 | C3×#41 | semidirect |
| 207. #67 | C3×C3⋊D3 | semidirect |
| 292. C32 | #3805 | semidirect |
| 293. C32 | C3×#237 | semidirect |
| 294. C32 | C3×#237 | semidirect |
| 295. C32 | #3830 | semidirect |
| 336. C3 | C3×#3805 | semidirect |
| 337. C3 | #89029 | direct (N × H) |
| 338. C3 | C3×#3830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(C3⋊Dic3) | 2 |
| C32×#638 | 2 |
| C33×#67 | 2 |
| C3×#6293 | 2 |
| C3×#6290 | 2 |
| C3×Dic3×C3⋊D3 | 2 |
| C3×D3×C3⋊Dic3 | 2 |
| C3×#3830 | 3 |
| #89029 | 3 |
| C3×#3805 | 3 |