Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
891 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 891 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #11720532 | C2 | direct (N × H) |
| 11. C2×#6229 | C4 | semidirect |
| 32. #6229 | C2×C4 | semidirect |
| 78. C2×H(3,𝔽3) | #103 | semidirect |
| 117. H(3,𝔽3) | C2×#103 | semidirect |
| 144. C2×C32 | #810 | semidirect |
| 177. C32 | C2×#810 | semidirect |
| 210. C2 | #11720532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6229 | 2 |
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C22×#6180 | 2 |
| #11720532 | 2 |
| C2×C3×#810 | 3 |