Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
908 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 166 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. #11723410 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C3×#63643 | C2 | semidirect |
| 7. #11722053 | C2 | semidirect |
| 21. #88792 | C4 | semidirect |
| 29. #63643 | D3 | semidirect |
| 44. C3×#634 | C2×C4 | semidirect |
| 50. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 87. C3⋊(C3⋊Dic3) | SD16 | semidirect |
| 124. #634 | C4×D3 | semidirect |
| 205. C33 | C4×SD16 | semidirect |
| 290. C32 | #4758 | semidirect |
| 291. C32 | #4788 | semidirect |
| 329. C3 | #10590742 | semidirect |
| 330. C3 | #10592457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723499 | 2 |
| #11723410 | 2 |
| C2×#88792 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| C3×#63643 | 2 |
| C32×#821 | 2 |
| #11722053 | 2 |
| #10592457 | 3 |
| #10590742 | 3 |