Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1024 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 190 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. C3×#64078 | C2 | semidirect |
| 3. C32×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #11722055 | C2 | semidirect |
| 20. #64078 | D3 | semidirect |
| 25. C3×C4⋊(C3⋊C8) | D3 | semidirect |
| 34. C4⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 84. C4⋊(C3⋊C8) | C3⋊D3 | semidirect |
| 177. C33 | #474 | semidirect |
| 259. C32 | #4846 | semidirect |
| 260. C32 | #5087 | semidirect |
| 295. C3 | #10590313 | semidirect |
| 296. C3 | #10592545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C3×#64078 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722055 | 2 |
| #11722036 | 2 |
| #10592545 | 3 |
| #10590313 | 3 |