Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
952 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 182 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. #11723501 | C2 | semidirect |
| 3. #11722185 | C2 | semidirect |
| 4. C32×#817 | C2 | semidirect |
| 5. #11722033 | C2 | semidirect |
| 13. C3×#3745 | C4 | semidirect |
| 25. C3×#817 | D3 | semidirect |
| 31. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 34. C33×C8 | C2×C4 | semidirect |
| 53. #3745 | Dic3 | semidirect |
| 71. #817 | C3⋊D3 | semidirect |
| 86. C4⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 93. C32×C8 | C4×D3 | semidirect |
| 94. C32×C8 | C2×Dic3 | semidirect |
| 146. C33 | #442 | semidirect |
| 164. C3×C8 | D3×Dic3 | semidirect |
| 165. C3×C8 | C4×C3⋊D3 | semidirect |
| 206. C32 | #4869 | semidirect |
| 207. C32 | #5152 | semidirect |
| 216. C8 | Dic3×C3⋊D3 | semidirect |
| 234. C3 | #10590781 | semidirect |
| 235. C3 | #10592568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| #11723501 | 2 |
| #11722185 | 2 |
| C32×#817 | 2 |
| #11722033 | 2 |
| #10592568 | 3 |
| #10590781 | 3 |