Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
752 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 166 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. C33×#135 | C2 | semidirect |
| 2. C3×#64113 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. C3×#63654 | C2 | semidirect |
| 6. C3×#63653 | C2 | semidirect |
| 7. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 8. #10592893 | C3 | direct (N × H) |
| 22. C32×#135 | D3 | semidirect |
| 23. C32×#135 | C2×C3 | semidirect |
| 24. #64113 | C2×C3 | semidirect |
| 26. #63656 | C2×C3 | semidirect |
| 27. #63655 | C2×C3 | semidirect |
| 28. #63654 | C2×C3 | semidirect |
| 29. #63653 | C2×C3 | semidirect |
| 30. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 85. C3×#135 | C3×D3 | semidirect |
| 86. C3×#135 | C3⋊D3 | semidirect |
| 179. #135 | C3×C3⋊D3 | semidirect |
| 185. C33 | #508 | semidirect |
| 257. C32 | #5194 | semidirect |
| 258. C32 | C3×#508 | semidirect |
| 289. C3 | C3×#5194 | semidirect |
| 290. C3 | #10592893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#135 | 2 |
| C3×#64113 | 2 |
| C3×#63656 | 2 |
| C3×#63655 | 2 |
| C3×#63654 | 2 |
| C3×#63653 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10592893 | 3 |
| C3×#5194 | 3 |