Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
891 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 891 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#88538 | C2 | semidirect |
| 4. #11720532 | C2 | semidirect |
| 5. #11720531 | C2 | semidirect |
| 11. #88740 | C4 | semidirect |
| 20. C2×C32×C4⋊C4 | D3 | semidirect |
| 35. C4⋊#272 | C2×C4 | semidirect |
| 38. #6229 | C2×C4 | semidirect |
| 136. C2×C4⋊C4 | #272 | semidirect |
| 139. H(3,𝔽3) | #417 | semidirect |
| 213. C32 | #4966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| #11720532 | 2 |
| #11720531 | 2 |
| C3×#4966 | 3 |