Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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. C3⋊(C3⋊(C3⋊C8)) | C8 | semidirect |
| 110. C33 | #334 | semidirect |
| 163. C32 | #4480 | semidirect |
| 164. C32 | #4480 | semidirect |
| 188. C3 | #10589098 | semidirect |
| 189. C3 | #10589346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #10589346 | 3 |
| #10589098 | 3 |