Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
979 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 979 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. C2×#88433 | C2 | direct (N × H) |
| 10. #88433 | C22 | direct (N × H) |
| 36. C22×H(3,𝔽3) | Q16 | semidirect |
| 64. C2×H(3,𝔽3) | C2×Q16 | semidirect |
| 85. C22×C32 | #216 | semidirect |
| 96. H(3,𝔽3) | C22×Q16 | semidirect |
| 120. C2×C32 | C2×#216 | semidirect |
| 144. C32 | C22×#216 | semidirect |
| 158. C22 | #88433 | direct (N × H) |
| 166. C2 | C2×#88433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634⋊C3 | 2 |
| C22×#6180 | 2 |
| C2×#88433 | 2 |
| C22×#3719 | 3 |