Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
210 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 35. C3⋊#622 | Q8 | semidirect |
| 36. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 37. C32×C3⋊C8 | Q8 | semidirect |
| 118. C33 | #501 | semidirect |
| 133. C3⋊C8 | PSU(3,𝔽2) | semidirect |
| 167. C32 | #5081 | semidirect |
| 197. C3 | #10593537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724361 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| #11722807 | 2 |
| #11722805 | 2 |
| #11722715 | 2 |
| #11722714 | 2 |
| #11722704 | 2 |
| #10593537 | 3 |
| #5081 | 9 |