Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 63 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. 2−1+4⋊H(3,𝔽3) | C2 | semidirect |
| 2. #11722577 | C2 | semidirect |
| 3. #131⋊H(3,𝔽3) | C2 | semidirect |
| 4. C32×#577 | C3 | semidirect |
| 5. C3×#577⋊C3 | C3 | semidirect |
| 11. C32×H(5,𝔽2) | C2×C3 | semidirect |
| 12. C3×2−1+4⋊C3 | C2×C3 | semidirect |
| 13. C3×#994 | C2×C3 | semidirect |
| 18. C32×#131 | C2×C3 | semidirect |
| 19. C3×#131⋊C3 | C2×C3 | semidirect |
| 88. #577 | H(3,𝔽3) | semidirect |
| 139. H(5,𝔽2) | C2×H(3,𝔽3) | semidirect |
| 144. #131 | C2×H(3,𝔽3) | semidirect |
| 226. C32 | #577⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 2−1+4⋊H(3,𝔽3) | 2 |
| #11722577 | 2 |
| #131⋊H(3,𝔽3) | 2 |
| C32×#577 | 3 |
| C3×#577⋊C3 | 3 |
| SD16×H(3,𝔽3) | 4 |