Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
736 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 212 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. #11722173 | C2 | semidirect |
| 3. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. Dic3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 22. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 131. C33 | #433 | semidirect |
| 184. C32 | #4690 | semidirect |
| 185. C32 | #5000 | semidirect |
| 210. C3 | #10590264 | semidirect |
| 211. C3 | #10592699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#872 | 2 |
| #11722173 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| Dic3⋊(C3⋊(C3⋊C8)) | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592699 | 3 |
| #10590264 | 3 |