Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2604 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2604 conjugacy classes of subgroups — too many to draw. Only its 851 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. #11722203 | C2 | direct (N × H) |
| 12. #88855 | C22 | semidirect |
| 68. C2×C33 | #100 | semidirect |
| 92. C33 | C2×#100 | semidirect |
| 108. C2×C32 | #833 | semidirect |
| 129. C32 | C2×#833 | semidirect |
| 145. C2×C3 | #63660 | semidirect |
| 157. C3 | C2×#63660 | semidirect |
| 161. C2 | #11722203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×#88855 | 2 |
| #11722203 | 2 |
| C2×#63660 | 3 |