Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
656 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 2. C33×C4⋊C8 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #10589351 | C3 | direct (N × H) |
| 15. C32×C4⋊C8 | D3 | semidirect |
| 16. C32×C4⋊C8 | C2×C3 | semidirect |
| 17. C4⋊(C3⋊(C3⋊C8)) | C2×C3 | semidirect |
| 59. C3×C4⋊C8 | C3×D3 | semidirect |
| 60. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 133. C4⋊C8 | C3×C3⋊D3 | semidirect |
| 134. C33 | #331 | semidirect |
| 203. C32 | #4485 | semidirect |
| 204. C32 | C3×#331 | semidirect |
| 237. C3 | C3×#4485 | semidirect |
| 238. C3 | #10589351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64083 | 2 |
| C33×C4⋊C8 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589351 | 3 |
| C3×#4485 | 3 |