Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
693 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 693 conjugacy classes of subgroups — too many to draw. Only its 249 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. C4⋊#6180 | C2 | semidirect |
| 38. C4×H(3,𝔽3) | M16 | semidirect |
| 78. C32×C4 | #208 | semidirect |
| 85. H(3,𝔽3) | #423 | semidirect |
| 130. C32 | #4924 | semidirect |
| 150. C4 | #88538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| C4⋊#6180 | 2 |
| C3×#4924 | 3 |