Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 851 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×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 3. C2×#88855 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 8. C33×#41 | C4 | semidirect |
| 27. C33×Q8 | C2×C4 | semidirect |
| 30. C33×D4 | C2×C4 | semidirect |
| 42. C32×#41 | Dic3 | semidirect |
| 73. C32×Q8 | C2×Dic3 | semidirect |
| 76. C32×D4 | C2×Dic3 | semidirect |
| 93. C3×#41 | C3⋊Dic3 | semidirect |
| 121. C33 | #417 | semidirect |
| 125. C3×Q8 | C2×C3⋊Dic3 | semidirect |
| 128. C3×D4 | C2×C3⋊Dic3 | semidirect |
| 144. #41 | C3⋊(C3⋊Dic3) | semidirect |
| 167. C32 | #5232 | semidirect |
| 171. Q8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 174. D4 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 201. C3 | #10592931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88855 | 2 |
| #11722205 | 2 |
| #11722202 | 2 |
| #10592931 | 3 |