Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
792 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. H(3,𝔽3)×#124 | C2 | semidirect |
| 2. C2×#88549 | C2 | semidirect |
| 3. C2×#88545 | C2 | semidirect |
| 4. #11721720 | C2 | semidirect |
| 5. #11720520 | C2 | semidirect |
| 16. C32×#124 | D3 | semidirect |
| 31. #6180 | D4 | semidirect |
| 106. #124 | #272 | semidirect |
| 108. H(3,𝔽3) | #496 | semidirect |
| 160. C32 | #5058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#124 | 2 |
| C2×#88549 | 2 |
| C2×#88545 | 2 |
| #11721720 | 2 |
| #11720520 | 2 |
| C3×#5058 | 3 |