Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2072 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 571 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×#88863 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 50. C22×C33 | Q16 | semidirect |
| 93. C22×C32 | #216 | semidirect |
| 105. C33 | #451 | semidirect |
| 136. C22×C3 | #3756 | semidirect |
| 143. C32 | #5228 | semidirect |
| 163. C22 | #88863 | semidirect |
| 170. C3 | #10592927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×#88863 | 2 |
| #11723965 | 2 |
| #11722205 | 2 |
| #11722200 | 2 |
| #10592927 | 3 |