Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
847 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 847 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. H(3,𝔽3)×#117 | C2 | semidirect |
| 3. C2×#88538 | C2 | semidirect |
| 4. #11720522 | C2 | semidirect |
| 10. #88740 | C4 | semidirect |
| 12. C2×C4⋊#272 | C4 | semidirect |
| 14. C2×#6229 | C4 | semidirect |
| 17. C42×H(3,𝔽3) | C22 | semidirect |
| 19. #88538 | C22 | semidirect |
| 22. C32×#117 | D3 | semidirect |
| 57. C32×C42 | C2×D3 | semidirect |
| 150. #117 | #272 | semidirect |
| 152. H(3,𝔽3) | #421 | semidirect |
| 210. C42 | C2×#272 | semidirect |
| 235. C32 | #5005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| H(3,𝔽3)×#117 | 2 |
| C2×#88538 | 2 |
| #11720522 | 2 |
| C3×#5005 | 3 |