Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
872 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 142 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. #11723989 | C2 | semidirect |
| 2. C3×#64160 | C2 | semidirect |
| 4. C2×#88792 | C2 | semidirect |
| 5. #11722059 | C2 | semidirect |
| 6. #11722029 | C2 | semidirect |
| 7. #11722025 | C2 | semidirect |
| 26. #64160 | D3 | semidirect |
| 224. C33 | #471 | semidirect |
| 313. C32 | #5200 | semidirect |
| 314. C32 | #5203 | semidirect |
| 351. C3 | #10591681 | semidirect |
| 352. C3 | #10592899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723989 | 2 |
| C3×#64160 | 2 |
| C32×#949 | 2 |
| C2×#88792 | 2 |
| #11722059 | 2 |
| #11722029 | 2 |
| #11722025 | 2 |
| #10592899 | 3 |
| #10591681 | 3 |