Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1650 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 1650 conjugacy classes of subgroups — too many to draw. Only its 339 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. #11720572 | C2 | semidirect |
| 10. C2×C4×C3⋊D9 | C4 | semidirect |
| 15. C9×#95 | D3 | semidirect |
| 22. C2×C3×C4×C9 | C2×C4 | semidirect |
| 24. C2×C3⋊Dic9 | C2×C4 | semidirect |
| 48. C3×#95 | D9 | semidirect |
| 66. C2×C4×C9 | C4×D3 | semidirect |
| 74. C3⋊D9 | #95 | direct (N × H) |
| 103. #95 | C3⋊D9 | direct (N × H) |
| 104. C3×C9 | C2×#95 | semidirect |
| 115. C2×C3×C4 | C4×D9 | semidirect |
| 153. C9 | D3×#95 | semidirect |
| 162. C2×C4 | C4×C3⋊D9 | semidirect |
| 179. C3 | D9×#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D9 | 2 |
| C3×C9×#95 | 2 |
| #11720572 | 2 |
| C3⋊D3×#95 | 3 |
| D9×#95 | 3 |