Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 234 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. C32×#869 | C2 | semidirect |
| 3. C33×#97 | C2 | semidirect |
| 5. C32×#816 | C2 | semidirect |
| 7. C3×#4714 | C3 | direct (N × H) |
| 20. C3×#869 | C2×C3 | semidirect |
| 24. C32×#97 | D3 | semidirect |
| 25. C32×#97 | C2×C3 | semidirect |
| 27. C3×#816 | C2×C3 | semidirect |
| 39. #4714 | C32 | direct (N × H) |
| 72. #869 | C2×C32 | semidirect |
| 76. C3×#97 | C3×D3 | semidirect |
| 77. C3×#97 | C2×C32 | semidirect |
| 79. #816 | C2×C32 | semidirect |
| 155. #97 | C32×D3 | semidirect |
| 156. C33 | #489 | semidirect |
| 224. C32 | #4714 | direct (N × H) |
| 225. C32 | C3×#489 | semidirect |
| 257. C3 | C3×#4714 | direct (N × H) |
| 258. C3 | C32×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#875 | 2 |
| C32×#869 | 2 |
| C33×#97 | 2 |
| C32×#821 | 2 |
| C32×#816 | 2 |
| C32×#489 | 3 |
| C3×#4714 | 3 |