Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
631 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 631 conjugacy classes of subgroups — too many to draw. Only its 59 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. C9⋊#997 | C2 | direct (N × H) |
| 3. C2×C9×H(5,𝔽2) | C3 | semidirect |
| 4. C2×#63703 | C3 | semidirect |
| 10. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 13. #63703 | C2×C3 | semidirect |
| 22. C24×C9 | A4 | semidirect |
| 28. C2×Q8×C9 | A4 | semidirect |
| 54. C23×C9 | C2×A4 | semidirect |
| 58. Q8×C9 | C2×A4 | semidirect |
| 67. C2×H(5,𝔽2) | 3−1+2 | semidirect |
| 102. H(5,𝔽2) | C2×3−1+2 | semidirect |
| 131. C2×C9 | #997 | semidirect |
| 134. C24 | C9⋊A4 | semidirect |
| 139. C2×Q8 | C9⋊A4 | semidirect |
| 161. C9 | C2×#997 | semidirect |
| 168. C23 | C2×C9⋊A4 | semidirect |
| 170. Q8 | C2×C9⋊A4 | semidirect |
| 198. C2 | C9⋊#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊#997 | 2 |
| C2×C3×#997 | 3 |
| C2×C9×H(5,𝔽2) | 3 |
| C2×#63703 | 3 |
| C22×C9⋊A4 | 4 |
| C2×C9⋊SL(2,𝔽3) | 4 |