Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2604 conjugacy classes of subgroups; only the 633 normal subgroups are shown.
This group has 2604 conjugacy classes of subgroups — too many to draw. Only its 633 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 |
| 4. C2×#88857 | C2 | semidirect |
| 5. #11722201 | C2 | semidirect |
| 16. C2×C32×C4⋊C4 | D3 | semidirect |
| 61. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 113. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 117. C33 | #399 | semidirect |
| 163. C32 | #4993 | semidirect |
| 200. C3 | #10592692 | 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 |
| C2×#88859 | 2 |
| C2×#88857 | 2 |
| #11722201 | 2 |
| #10592692 | 3 |