Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 118 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×H(5,𝔽2) | C2 | semidirect |
| 2. C3×#63499 | C2 | semidirect |
| 3. C3×#63393 | C2 | semidirect |
| 5. #10588924 | C3 | direct (N × H) |
| 6. C23×C3×D9 | C22 | semidirect |
| 11. C3×#3676 | C22 | semidirect |
| 16. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 18. #63499 | C2×C3 | semidirect |
| 19. #63393 | C2×C3 | semidirect |
| 21. C23×C3×C9 | D4 | semidirect |
| 29. C2×C3×C4×C9 | D4 | semidirect |
| 39. C23×D9 | C22×C3 | semidirect |
| 49. #3676 | C22×C3 | semidirect |
| 62. C3×H(5,𝔽2) | D9 | semidirect |
| 84. C23×C9 | C3×D4 | semidirect |
| 97. C2×C4×C9 | C3×D4 | semidirect |
| 148. H(5,𝔽2) | C3×D9 | semidirect |
| 151. C3×C9 | B(4,𝔽2) | semidirect |
| 159. C23×C3 | #611 | semidirect |
| 180. C2×C3×C4 | #611 | semidirect |
| 230. C9 | C3×B(4,𝔽2) | semidirect |
| 234. C23 | C3×#611 | semidirect |
| 242. C2×C4 | C3×#611 | semidirect |
| 265. C3 | #10588924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| C3×#63499 | 2 |
| C3×#63393 | 2 |
| C3×#5244 | 3 |
| #10588924 | 3 |