Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
740 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 154 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×C22⋊C8 | C2 | semidirect |
| 3. C3×#63658 | C2 | semidirect |
| 4. #10589336 | C3 | direct (N × H) |
| 9. C2×C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 12. C3×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 16. C32×C22⋊C8 | D3 | semidirect |
| 17. C32×C22⋊C8 | C2×C3 | semidirect |
| 18. #63658 | C2×C3 | semidirect |
| 40. C2×C4⋊(C3⋊D3) | C3×C4 | semidirect |
| 48. C4⋊(C3⋊Dic3) | C3×C4 | semidirect |
| 66. C3×C22⋊C8 | C3×D3 | semidirect |
| 67. C3×C22⋊C8 | C3⋊D3 | semidirect |
| 156. C22⋊C8 | C3×C3⋊D3 | semidirect |
| 158. C33 | #327 | semidirect |
| 246. C32 | #4470 | semidirect |
| 247. C32 | C3×#327 | semidirect |
| 291. C3 | C3×#4470 | semidirect |
| 292. C3 | #10589336 | 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 |
| C33×C22⋊C8 | 2 |
| C3×#63658 | 2 |
| #10589336 | 3 |
| C3×#4470 | 3 |