Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3724 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3724 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 |
|---|---|---|
| 1. C2×#89080 | C2 | semidirect |
| 2. C2×#89078 | C2 | semidirect |
| 3. C2×C33×SD16 | C2 | semidirect |
| 4. C2×#88863 | C2 | semidirect |
| 5. C2×#88860 | C2 | semidirect |
| 6. #11723957 | C2 | direct (N × H) |
| 7. C2×#88851 | C2 | semidirect |
| 8. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 15. #89080 | C22 | semidirect |
| 17. #89078 | C22 | semidirect |
| 23. C33×SD16 | C22 | semidirect |
| 25. #88863 | C22 | semidirect |
| 26. #88860 | C22 | semidirect |
| 28. #88851 | C22 | semidirect |
| 29. C8×C3⋊(C3⋊D3) | C22 | semidirect |
| 32. C2×C32×SD16 | D3 | semidirect |
| 75. C32×SD16 | C2×D3 | semidirect |
| 96. C2×C3×SD16 | C3⋊D3 | semidirect |
| 127. C2×C33 | #135 | semidirect |
| 144. C3×SD16 | C2×C3⋊D3 | semidirect |
| 168. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 171. C33 | C2×#135 | semidirect |
| 196. C2×C32 | #916 | semidirect |
| 215. SD16 | C2×C3⋊(C3⋊D3) | semidirect |
| 232. C32 | C2×#916 | semidirect |
| 257. C2×C3 | #64125 | semidirect |
| 273. C3 | C2×#64125 | semidirect |
| 277. C2 | #11723957 | 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×#89078 | 2 |
| C2×C33×SD16 | 2 |
| C2×#88863 | 2 |
| C2×#88860 | 2 |
| #11723957 | 2 |
| C2×#88851 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C2×#64125 | 3 |