Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 419 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 419 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×#88850 | C2 | semidirect |
| 3. C4⋊C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 4. C33×#103 | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 11. #89080 | C4 | semidirect |
| 26. C32×#103 | D3 | semidirect |
| 33. C33×Q8 | C2×C4 | semidirect |
| 41. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 79. C3×#103 | C3⋊D3 | semidirect |
| 86. C32×Q8 | C4×D3 | semidirect |
| 138. #103 | C3⋊(C3⋊D3) | semidirect |
| 141. C33 | #417 | semidirect |
| 145. C3×Q8 | C4×C3⋊D3 | semidirect |
| 192. C32 | #4803 | semidirect |
| 196. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 229. C3 | #10592502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C2×#88850 | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C33×#103 | 2 |
| #11722205 | 2 |
| #11722191 | 2 |
| #11722179 | 2 |
| #10592502 | 3 |