Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1344 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 22. C33×Q8 | Q8 | semidirect |
| 55. C32×Q8 | Dic6 | semidirect |
| 90. C33 | #475 | semidirect |
| 92. C3×Q8 | #634 | semidirect |
| 121. C32 | #5020 | semidirect |
| 124. Q8 | #6308 | semidirect |
| 143. C3 | #10592719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| #11723910 | 2 |
| #11722205 | 2 |
| #11722178 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592719 | 3 |