Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
727 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 727 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. C2×#88631 | C2 | semidirect |
| 3. C22×#6188 | C2 | semidirect |
| 4. #11722449 | C2 | direct (N × H) |
| 5. C2×#88627 | C2 | semidirect |
| 6. C2×#88626 | C2 | semidirect |
| 14. #88631 | C22 | semidirect |
| 18. C2×#6188 | C22 | semidirect |
| 19. #88627 | C22 | semidirect |
| 20. #88626 | C22 | semidirect |
| 75. C2×H(3,𝔽3) | #131 | semidirect |
| 114. H(3,𝔽3) | C2×#131 | semidirect |
| 215. C2 | #11722449 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88744 | 2 |
| C2×#88631 | 2 |
| C22×#6188 | 2 |
| #11722449 | 2 |
| C2×#88627 | 2 |
| C2×#88626 | 2 |
| C2×C3×#131 | 9 |