Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2044 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2044 conjugacy classes of subgroups — too many to draw. Only its 635 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 |
|---|---|---|
| 4. #11722194 | C2 | direct (N × H) |
| 87. C2×C33 | #101 | semidirect |
| 116. C33 | C2×#101 | semidirect |
| 135. C2×C32 | #824 | semidirect |
| 160. C32 | C2×#824 | semidirect |
| 179. C2×C3 | #63651 | semidirect |
| 190. C3 | C2×#63651 | semidirect |
| 193. C2 | #11722194 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| #11722194 | 2 |
| C2×#63651 | 3 |