Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 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. #11724238 | C2 | semidirect |
| 3. C3×#64213 | C2 | semidirect |
| 4. #11724094 | C2 | semidirect |
| 5. #11724092 | C2 | semidirect |
| 19. #64213 | D3 | semidirect |
| 92. C33 | #504 | semidirect |
| 137. C32 | #4901 | semidirect |
| 161. C3 | #10596487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724252 | 2 |
| #11724238 | 2 |
| C3×#64213 | 2 |
| #11724094 | 2 |
| #11724092 | 2 |
| #10596487 | 3 |
| #4901 | 9 |