Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1066 conjugacy classes of subgroups; only the 314 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 314 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. C3×C9×#95 | C2 | semidirect |
| 3. C3×C9⋊#95 | C2 | semidirect |
| 5. D9×#95 | C3 | direct (N × H) |
| 10. C2×C3×C4×D9 | C4 | semidirect |
| 16. C9×#95 | C2×C3 | semidirect |
| 17. C9⋊#95 | C2×C3 | semidirect |
| 23. C2×C3×C4×C9 | C2×C4 | semidirect |
| 25. C2×C3×Dic9 | C2×C4 | semidirect |
| 39. C2×C4×D9 | C3×C4 | semidirect |
| 52. C3×#95 | D9 | direct (N × H) |
| 72. C2×C4×C9 | C2×C3×C4 | semidirect |
| 74. C2×Dic9 | C2×C3×C4 | semidirect |
| 80. C3×D9 | #95 | direct (N × H) |
| 114. #95 | C3×D9 | direct (N × H) |
| 115. C3×C9 | C2×#95 | semidirect |
| 132. C2×C3×C4 | C4×D9 | semidirect |
| 147. D9 | C3×#95 | direct (N × H) |
| 175. C9 | C2×C3×#95 | semidirect |
| 184. C2×C4 | C3×C4×D9 | semidirect |
| 205. C3 | D9×#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D9 | 2 |
| C3×C9×#95 | 2 |
| C3×C9⋊#95 | 2 |
| C3×D3×#95 | 3 |
| D9×#95 | 3 |