Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 182 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. C33×C4⋊C8 | C2 | semidirect |
| 3. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10589349 | C3 | direct (N × H) |
| 16. C32×C4⋊C8 | D3 | semidirect |
| 17. C32×C4⋊C8 | C2×C3 | semidirect |
| 18. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 26. C3×C4⋊(C3⋊D3) | C8 | semidirect |
| 62. C3×C4⋊C8 | C3×D3 | semidirect |
| 63. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 79. C4⋊(C3⋊D3) | C3×C8 | semidirect |
| 140. C4⋊C8 | C3×C3⋊D3 | semidirect |
| 142. C33 | D4⋊C8 | semidirect |
| 214. C32 | #4483 | semidirect |
| 215. C32 | C3×D4⋊C8 | semidirect |
| 249. C3 | C3×#4483 | semidirect |
| 250. C3 | #10589349 | direct (N × H) |
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 |
| C33×C4⋊C8 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10589349 | 3 |
| C3×#4483 | 3 |