Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2128 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 2128 conjugacy classes of subgroups — too many to draw. Only its 407 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×Q16 | C2 | semidirect |
| 3. #11723987 | C2 | semidirect |
| 4. C2×#88862 | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722190 | C2 | semidirect |
| 25. C2×C32×Q16 | D3 | semidirect |
| 80. C2×C3×Q16 | C3⋊D3 | semidirect |
| 140. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 146. C33 | #452 | semidirect |
| 199. C32 | #5187 | semidirect |
| 237. C3 | #10592886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C2×C33×Q16 | 2 |
| #11723987 | 2 |
| C2×#88862 | 2 |
| #11722205 | 2 |
| #11722191 | 2 |
| #11722190 | 2 |
| #10592886 | 3 |