Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3388 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3388 conjugacy classes of subgroups — too many to draw. Only its 891 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 |
|---|---|---|
| 3. #11723965 | C2 | semidirect |
| 4. #11723919 | C2 | semidirect |
| 9. C2×#6308 | C22 | semidirect |
| 13. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 14. #88857 | C22 | semidirect |
| 20. C23×C33 | Q8 | semidirect |
| 51. C23×C32 | Dic6 | semidirect |
| 85. C33 | #543 | semidirect |
| 87. C23×C3 | #634 | semidirect |
| 116. C32 | #5483 | semidirect |
| 118. C23 | #6308 | semidirect |
| 138. C3 | #10595954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C22⋊C4 | 2 |
| C2×#88864 | 2 |
| #11723965 | 2 |
| #11723919 | 2 |
| #10595954 | 3 |