Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
322 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C2×C9×D24 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 4. #11720238 | C2 | direct (N × H) |
| 11. C9×D24 | C22 | semidirect |
| 13. C3×D72 | C22 | semidirect |
| 14. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C2×D72 | D3 | semidirect |
| 50. D72 | C2×D3 | semidirect |
| 63. C2×D24 | D9 | semidirect |
| 91. C2×C3×C9 | D16 | semidirect |
| 109. D24 | C2×D9 | semidirect |
| 134. C3×C9 | C2×D16 | semidirect |
| 163. C2×C9 | #826 | semidirect |
| 193. C9 | C2×#826 | semidirect |
| 207. C2×C3 | #63385 | semidirect |
| 221. C3 | C2×#63385 | semidirect |
| 225. C2 | #11720238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C2×C3×D72 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #11720238 | 2 |
| C2×#63545 | 3 |
| C2×#63385 | 3 |