Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2072 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 463 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 |
|---|---|---|
| 3. C2×#88863 | C2 | semidirect |
| 5. #11722180 | C2 | semidirect |
| 50. C22×C33 | Q16 | semidirect |
| 93. C22×C32 | #216 | semidirect |
| 105. C33 | #451 | semidirect |
| 136. C22×C3 | #3756 | semidirect |
| 143. C32 | #5050 | semidirect |
| 163. C22 | #88863 | semidirect |
| 170. C3 | #10592749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C33×C22⋊Q8 | 2 |
| C2×#88863 | 2 |
| #11722200 | 2 |
| #11722180 | 2 |
| #10592749 | 3 |