Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2968 conjugacy classes of subgroups; only the 723 normal subgroups are shown.
This group has 2968 conjugacy classes of subgroups — too many to draw. Only its 723 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 |
|---|---|---|
| 1. C33×C4×Q8 | C2 | semidirect |
| 2. #11723987 | C2 | semidirect |
| 3. #11723939 | C2 | semidirect |
| 4. #11723933 | C2 | semidirect |
| 7. #11723910 | C2 | semidirect |
| 8. C4×#6308 | C2 | semidirect |
| 26. C32×C4×Q8 | D3 | semidirect |
| 74. C3×C4×Q8 | C3⋊D3 | semidirect |
| 131. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #556 | semidirect |
| 178. C32 | #5584 | semidirect |
| 206. C3 | #10596055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| #11723987 | 2 |
| #11723939 | 2 |
| #11723933 | 2 |
| #11723916 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723910 | 2 |
| C4×#6308 | 2 |
| #10596055 | 3 |