Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1852 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 1852 conjugacy classes of subgroups — too many to draw. Only its 214 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. C33×H(5,𝔽2) | C2 | semidirect |
| 2. C3×#64146 | C2 | semidirect |
| 3. C3×#63661 | C2 | semidirect |
| 4. #10592943 | C3 | direct (N × H) |
| 6. C23×C3×C3⋊D3 | C22 | semidirect |
| 11. C3×#3757 | C22 | semidirect |
| 14. C32×H(5,𝔽2) | D3 | semidirect |
| 15. C32×H(5,𝔽2) | C2×C3 | semidirect |
| 16. #64146 | C2×C3 | semidirect |
| 18. #63661 | C2×C3 | semidirect |
| 21. C23×C33 | D4 | semidirect |
| 29. C2×C33×C4 | D4 | semidirect |
| 34. C23×C3⋊D3 | C22×C3 | semidirect |
| 47. #3757 | C22×C3 | semidirect |
| 62. C3×H(5,𝔽2) | C3×D3 | semidirect |
| 63. C3×H(5,𝔽2) | C3⋊D3 | semidirect |
| 73. C23×C32 | #67 | semidirect |
| 74. C23×C32 | C3×D4 | semidirect |
| 94. C2×C32×C4 | #67 | semidirect |
| 95. C2×C32×C4 | C3×D4 | semidirect |
| 148. H(5,𝔽2) | C3×C3⋊D3 | semidirect |
| 151. C33 | B(4,𝔽2) | semidirect |
| 159. C23×C3 | C3×#67 | semidirect |
| 160. C23×C3 | #638 | semidirect |
| 180. C2×C3×C4 | C3×#67 | semidirect |
| 181. C2×C3×C4 | #638 | semidirect |
| 229. C32 | #5244 | semidirect |
| 230. C32 | C3×B(4,𝔽2) | semidirect |
| 234. C23 | C3×#638 | semidirect |
| 242. C2×C4 | C3×#638 | semidirect |
| 265. C3 | C3×#5244 | semidirect |
| 266. C3 | #10592943 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×H(5,𝔽2) | 2 |
| C3×#64146 | 2 |
| C3×#63661 | 2 |
| #10592943 | 3 |
| C3×#5244 | 3 |