Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 214 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. C2×C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C33×C22⋊C8 | C2 | semidirect |
| 4. C3×#63648 | C2 | semidirect |
| 5. C3×#63644 | C2 | semidirect |
| 6. #10592434 | C3 | direct (N × H) |
| 18. C2×C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 22. C32×C22⋊C8 | D3 | semidirect |
| 23. C32×C22⋊C8 | C2×C3 | semidirect |
| 24. #63648 | C2×C3 | semidirect |
| 25. #63644 | C2×C3 | semidirect |
| 79. C3×C22⋊C8 | C3×D3 | semidirect |
| 80. C3×C22⋊C8 | C3⋊D3 | semidirect |
| 168. C22⋊C8 | C3×C3⋊D3 | semidirect |
| 169. C33 | #481 | semidirect |
| 249. C32 | #4735 | semidirect |
| 250. C32 | C3×#481 | semidirect |
| 288. C3 | C3×#4735 | semidirect |
| 289. C3 | #10592434 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64139 | 2 |
| C2×C3×C4⋊(C3⋊Dic3) | 2 |
| C33×C22⋊C8 | 2 |
| C3×#63648 | 2 |
| C3×#63644 | 2 |
| #10592434 | 3 |
| C3×#4735 | 3 |