Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 131 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×C9×#135 | C2 | semidirect |
| 2. C2×#88525 | C2 | semidirect |
| 3. #11720567 | C2 | semidirect |
| 4. #11720563 | C2 | semidirect |
| 5. #11720534 | C2 | semidirect |
| 10. C3×C9×Q16 | C22 | semidirect |
| 12. C3×C9×D8 | C22 | semidirect |
| 16. C3⋊(C9⋊C16) | C22 | semidirect |
| 22. C9×#135 | D3 | semidirect |
| 50. C9×Q16 | C2×D3 | semidirect |
| 52. C9×D8 | C2×D3 | semidirect |
| 64. C3×#135 | D9 | semidirect |
| 103. C3×Q16 | C2×D9 | semidirect |
| 107. C3×D8 | C2×D9 | semidirect |
| 131. #135 | C3⋊D9 | semidirect |
| 136. C3×C9 | #509 | semidirect |
| 167. Q16 | C2×C3⋊D9 | semidirect |
| 171. D8 | C2×C3⋊D9 | semidirect |
| 189. C9 | #5193 | semidirect |
| 215. C3 | #10588873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#135 | 2 |
| C2×#88525 | 2 |
| #11720567 | 2 |
| #11720563 | 2 |
| #11720534 | 2 |
| #10592892 | 3 |
| #10588873 | 3 |