Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1098 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 262 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. C3×#63700 | C2 | semidirect |
| 3. C2×C3×#41⋊C9 | C2 | semidirect |
| 5. #10593120 | C3 | direct (N × H) |
| 7. C3×#41⋊C9 | C22 | semidirect |
| 8. C3×#41⋊C9 | C22 | semidirect |
| 9. C2×C3×Q8⋊C9 | C22 | semidirect |
| 17. 2−1+4⋊C9 | C2×C3 | semidirect |
| 18. #63700 | C2×C3 | semidirect |
| 19. C2×#41⋊C9 | C2×C3 | semidirect |
| 24. C3×#585 | C9 | semidirect |
| 46. #41⋊C9 | C22×C3 | semidirect |
| 47. #41⋊C9 | C22×C3 | semidirect |
| 48. C2×Q8⋊C9 | C22×C3 | semidirect |
| 54. C3×2−1+4 | C2×C9 | semidirect |
| 58. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 64. C2×C3×#41 | C2×C9 | semidirect |
| 89. #585 | C3×C9 | semidirect |
| 143. 2−1+4 | C2×C3×C9 | semidirect |
| 145. H(5,𝔽2) | C2×C3×C9 | semidirect |
| 148. C2×#41 | C2×C3×C9 | semidirect |
| 269. C3 | #10593120 | direct (N × H) |
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 |
| C3×#63700 | 2 |
| C2×C3×#41⋊C9 | 2 |
| C32×#585 | 3 |
| #10593120 | 3 |
| C3×C9×#41 | 4 |