Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 192 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. C32×#869 | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 4. #11722056 | C2 | semidirect |
| 20. C3×#869 | D3 | semidirect |
| 34. C3×C4⋊(C3⋊D3) | Q8 | semidirect |
| 74. #869 | C3⋊D3 | semidirect |
| 97. C4⋊(C3⋊D3) | Dic6 | semidirect |
| 163. C33 | #474 | semidirect |
| 236. C32 | #5007 | semidirect |
| 237. C32 | #5087 | semidirect |
| 271. C3 | #10590269 | semidirect |
| 272. C3 | #10592786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊(C3⋊D3) | 2 |
| C32×#869 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722056 | 2 |
| #11722033 | 2 |
| #10592786 | 3 |
| #10590269 | 3 |