Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1111 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1111 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 |
|---|---|---|
| 2. C2×C4⋊C4×H(3,𝔽3) | C2 | semidirect |
| 3. C22×#6180 | C2 | semidirect |
| 4. #11720531 | C2 | direct (N × H) |
| 11. C2×C4⋊#272 | C4 | semidirect |
| 14. C4⋊C4×H(3,𝔽3) | C22 | semidirect |
| 16. C2×#6180 | C22 | semidirect |
| 18. C2×C32×C4⋊C4 | D3 | semidirect |
| 34. C4⋊#272 | C2×C4 | semidirect |
| 46. C32×C4⋊C4 | C2×D3 | semidirect |
| 85. C2×H(3,𝔽3) | #102 | semidirect |
| 126. C2×C4⋊C4 | #272 | semidirect |
| 128. H(3,𝔽3) | C2×#102 | semidirect |
| 159. C2×C32 | #809 | semidirect |
| 174. C4⋊C4 | C2×#272 | semidirect |
| 199. C32 | C2×#809 | semidirect |
| 240. C2 | #11720531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C22×#6180 | 2 |
| #11720531 | 2 |
| C2×C3×#809 | 3 |