Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
657 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 163 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. #11722559 | C2 | semidirect |
| 2. #11722557 | C2 | semidirect |
| 3. C2×#88683 | C2 | semidirect |
| 5. C9×#585 | C3 | semidirect |
| 6. #10593120 | C3 | semidirect |
| 8. #88683 | C22 | semidirect |
| 9. #88683 | C22 | semidirect |
| 10. C2×C9⋊SL(2,𝔽3) | C22 | semidirect |
| 15. C9×2−1+4 | C2×C3 | semidirect |
| 17. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 20. C2×C9×#41 | C2×C3 | semidirect |
| 21. 2−1+4⋊C9 | C2×C3 | semidirect |
| 22. #63700 | C2×C3 | semidirect |
| 23. C2×#41⋊C9 | C2×C3 | semidirect |
| 97. #585 | 3−1+2 | semidirect |
| 139. 2−1+4 | C2×3−1+2 | semidirect |
| 141. H(5,𝔽2) | C2×3−1+2 | semidirect |
| 144. C2×#41 | C2×3−1+2 | semidirect |
| 210. C9 | #5945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722559 | 2 |
| #11722557 | 2 |
| C2×#88683 | 2 |
| C3×#5945 | 3 |
| C9×#585 | 3 |
| #10593120 | 3 |
| #41×3−1+2 | 4 |