Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1490 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
This group has 1490 conjugacy classes of subgroups — too many to draw. Only its 431 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 |
|---|---|---|
| 2. C22×#6226 | C2 | semidirect |
| 3. C22×C3×C8×C9 | C2 | semidirect |
| 4. C2×#88524 | C2 | direct (N × H) |
| 13. C2×#6226 | C22 | semidirect |
| 14. C2×C3×C8×C9 | C22 | semidirect |
| 15. #88524 | C22 | direct (N × H) |
| 22. C22×C8×C9 | D3 | semidirect |
| 33. #6226 | C23 | semidirect |
| 34. C3×C8×C9 | C23 | semidirect |
| 53. C2×C8×C9 | C2×D3 | semidirect |
| 55. C22×C3×C9 | SD16 | semidirect |
| 66. C22×C3×C8 | D9 | semidirect |
| 91. C8×C9 | C22×D3 | semidirect |
| 93. C2×C3×C9 | C2×SD16 | semidirect |
| 110. C2×C3×C8 | C2×D9 | semidirect |
| 121. C22×C9 | #204 | semidirect |
| 131. C22×C8 | C3⋊D9 | semidirect |
| 132. C3×C9 | C22×SD16 | semidirect |
| 153. C3×C8 | C22×D9 | semidirect |
| 158. C2×C9 | C2×#204 | semidirect |
| 169. C2×C8 | C2×C3⋊D9 | semidirect |
| 170. C22×C3 | #3664 | semidirect |
| 185. C9 | C22×#204 | semidirect |
| 196. C8 | C22×C3⋊D9 | semidirect |
| 197. C2×C3 | C2×#3664 | semidirect |
| 205. C22 | #88524 | direct (N × H) |
| 210. C3 | C22×#3664 | semidirect |
| 213. C2 | C2×#88524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C22×#6226 | 2 |
| C22×C3×C8×C9 | 2 |
| C2×#88524 | 2 |
| C22×#3744 | 3 |
| C22×#3664 | 3 |