Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2660 conjugacy classes of subgroups; only the 963 normal subgroups are shown.
This group has 2660 conjugacy classes of subgroups — too many to draw. Only its 963 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×#88855 | C2 | semidirect |
| 3. #11722200 | C2 | semidirect |
| 12. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 42. C22×C33 | M16 | semidirect |
| 79. C22×C32 | #208 | semidirect |
| 88. C33 | #407 | semidirect |
| 117. C22×C3 | #3748 | semidirect |
| 123. C32 | #5207 | semidirect |
| 144. C22 | #88855 | semidirect |
| 150. C3 | #10592906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C2×#88855 | 2 |
| #11722200 | 2 |
| #10592906 | 3 |