Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
754 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 109 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. C3×2−1+4⋊C9 | C2 | semidirect |
| 2. D3×#41⋊C9 | C2 | semidirect |
| 3. C3⋊#63700 | C2 | semidirect |
| 4. #1007⋊C9 | C2 | semidirect |
| 5. C2×C3⋊(#41⋊C9) | C2 | semidirect |
| 9. C3×#41⋊C9 | C22 | semidirect |
| 10. C2×C3×Q8⋊C9 | C22 | semidirect |
| 11. D3×Q8⋊C9 | C22 | semidirect |
| 12. C3⋊(#41⋊C9) | C22 | semidirect |
| 13. C3⋊(#41⋊C9) | C22 | semidirect |
| 27. 2−1+4⋊C9 | D3 | semidirect |
| 38. #5968 | C9 | semidirect |
| 77. #41⋊C9 | C2×D3 | semidirect |
| 80. C2×Q8⋊C9 | C2×D3 | semidirect |
| 89. C3×2−1+4 | C2×C9 | semidirect |
| 101. #1009 | C2×C9 | semidirect |
| 104. D3×#41 | C2×C9 | semidirect |
| 106. #1007 | C2×C9 | semidirect |
| 108. C2×#239 | C2×C9 | semidirect |
| 251. 2−1+4 | D3×C9 | semidirect |
| 483. C3 | #10593120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+4⋊C9 | 2 |
| D3×#41⋊C9 | 2 |
| C3⋊#63700 | 2 |
| #1007⋊C9 | 2 |
| C2×C3⋊(#41⋊C9) | 2 |
| C3×#5968 | 3 |
| #10593120 | 3 |
| C9×#237 | 4 |