Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
752 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 752 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×#870 | C2 | semidirect |
| 3. C33×C4×C8 | C2 | semidirect |
| 5. C32×#816 | C2 | semidirect |
| 7. C3×#4697 | C3 | direct (N × H) |
| 18. C3×#870 | C2×C3 | semidirect |
| 22. C32×C4×C8 | D3 | semidirect |
| 23. C32×C4×C8 | C2×C3 | semidirect |
| 25. C3×#816 | C2×C3 | semidirect |
| 35. #4697 | C32 | direct (N × H) |
| 62. #870 | C2×C32 | semidirect |
| 66. C3×C4×C8 | C3×D3 | semidirect |
| 67. C3×C4×C8 | C2×C32 | semidirect |
| 69. #816 | C2×C32 | semidirect |
| 130. C4×C8 | C32×D3 | semidirect |
| 131. C33 | #488 | semidirect |
| 184. C32 | #4697 | direct (N × H) |
| 185. C32 | C3×#488 | semidirect |
| 210. C3 | C3×#4697 | direct (N × H) |
| 211. C3 | C32×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#875 | 2 |
| C32×#870 | 2 |
| C33×C4×C8 | 2 |
| C32×#821 | 2 |
| C32×#816 | 2 |
| C32×#488 | 3 |
| C3×#4697 | 3 |