Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
677 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 677 conjugacy classes of subgroups — too many to draw. Only its 102 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. 3−1+2×H(5,𝔽2) | C2 | semidirect |
| 2. #63499⋊C3 | C2 | semidirect |
| 3. #63393⋊C3 | C2 | semidirect |
| 5. #10588924 | C3 | semidirect |
| 6. C23×AGL(1,ℤ/9) | C22 | semidirect |
| 11. #3676⋊C3 | C22 | semidirect |
| 16. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 18. #63499 | C2×C3 | semidirect |
| 19. #63393 | C2×C3 | semidirect |
| 21. C23×3−1+2 | D4 | semidirect |
| 29. C2×C4×3−1+2 | D4 | semidirect |
| 39. C23×D9 | C22×C3 | semidirect |
| 49. #3676 | C22×C3 | semidirect |
| 83. C23×C9 | C3×D4 | semidirect |
| 96. C2×C4×C9 | C3×D4 | semidirect |
| 144. H(5,𝔽2) | AGL(1,ℤ/9) | semidirect |
| 147. 3−1+2 | B(4,𝔽2) | semidirect |
| 212. C9 | C3×B(4,𝔽2) | semidirect |
| 216. C23 | #611⋊C3 | semidirect |
| 224. C2×C4 | #611⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×H(5,𝔽2) | 2 |
| #63499⋊C3 | 2 |
| #63393⋊C3 | 2 |
| C3×#5244 | 3 |
| #10588924 | 3 |