Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 675 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×Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×C33×Q16 | C2 | semidirect |
| 4. C2×#88863 | C2 | semidirect |
| 5. C2×#88862 | C2 | semidirect |
| 6. #11723959 | C2 | direct (N × H) |
| 7. C2×#88851 | C2 | semidirect |
| 8. C2×#88850 | C2 | semidirect |
| 15. Q8×C3⋊(C3⋊D3) | C22 | semidirect |
| 23. C33×Q16 | C22 | semidirect |
| 25. #88863 | C22 | semidirect |
| 26. #88862 | C22 | semidirect |
| 28. #88851 | C22 | semidirect |
| 29. #88850 | C22 | semidirect |
| 32. C2×C32×Q16 | D3 | semidirect |
| 75. C32×Q16 | C2×D3 | semidirect |
| 95. C2×C3×Q16 | C3⋊D3 | semidirect |
| 125. C2×C33 | #137 | semidirect |
| 142. C3×Q16 | C2×C3⋊D3 | semidirect |
| 164. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 168. C33 | C2×#137 | semidirect |
| 192. C2×C32 | #918 | semidirect |
| 210. Q16 | C2×C3⋊(C3⋊D3) | semidirect |
| 227. C32 | C2×#918 | semidirect |
| 251. C2×C3 | #64127 | semidirect |
| 266. C3 | C2×#64127 | semidirect |
| 269. C2 | #11723959 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C2×C33×Q16 | 2 |
| C2×#88863 | 2 |
| C2×#88862 | 2 |
| #11723959 | 2 |
| C2×#88851 | 2 |
| C2×#88850 | 2 |
| C2×#64127 | 3 |