Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
226 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 28. C3⋊#622 | Q8 | semidirect |
| 29. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 30. C32×C3⋊C8 | Q8 | semidirect |
| 98. C33 | #500 | semidirect |
| 112. C3⋊C8 | PSU(3,𝔽2) | semidirect |
| 142. C32 | #5078 | semidirect |
| 169. C3 | #10593536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724365 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| #11722807 | 2 |
| #11722715 | 2 |
| C3⋊C8×#157 | 2 |
| #10593536 | 3 |
| #5078 | 9 |