Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2100 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 579 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×C33×M16 | C2 | semidirect |
| 3. C2×#88855 | C2 | semidirect |
| 4. #11722194 | C2 | semidirect |
| 5. #11722193 | C2 | semidirect |
| 23. C2×C32×M16 | D3 | semidirect |
| 74. C2×C3×M16 | C3⋊D3 | semidirect |
| 131. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #413 | semidirect |
| 185. C32 | #5132 | semidirect |
| 221. C3 | #10592831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| #11722194 | 2 |
| #11722193 | 2 |
| #10592831 | 3 |