Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3052 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3052 conjugacy classes of subgroups — too many to draw. Only its 667 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. C2×C33×C4⋊C4 | C2 | semidirect |
| 3. #11723970 | C2 | semidirect |
| 4. C4×#6312 | C2 | semidirect |
| 5. #11723965 | C2 | semidirect |
| 6. #11723939 | C2 | semidirect |
| 7. #11723937 | C2 | semidirect |
| 8. #11723935 | C2 | semidirect |
| 9. #11723930 | C2 | semidirect |
| 32. C2×C32×C4⋊C4 | D3 | semidirect |
| 93. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 167. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 168. C33 | #539 | semidirect |
| 225. C32 | #5515 | semidirect |
| 261. C3 | #10595986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| #11723971 | 2 |
| #11723970 | 2 |
| C4×#6312 | 2 |
| #11723965 | 2 |
| #11723939 | 2 |
| #11723937 | 2 |
| #11723935 | 2 |
| #11723930 | 2 |
| #10595986 | 3 |