Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 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×#88525 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. C2×C9×C3⋊C16 | C2 | semidirect |
| 4. #11720232 | C2 | direct (N × H) |
| 11. #88525 | C22 | semidirect |
| 13. C3×D72 | C22 | semidirect |
| 14. C9×C3⋊C16 | C22 | semidirect |
| 21. C2×D72 | D3 | semidirect |
| 53. D72 | C2×D3 | semidirect |
| 69. C2×C3⋊C16 | D9 | semidirect |
| 96. C2×C3×C9 | D16 | semidirect |
| 119. C3⋊C16 | C2×D9 | semidirect |
| 143. C3×C9 | C2×D16 | semidirect |
| 174. C2×C9 | #826 | semidirect |
| 208. C9 | C2×#826 | semidirect |
| 221. C2×C3 | D144 | semidirect |
| 237. C3 | C2×D144 | semidirect |
| 241. C2 | #11720232 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C3×D72 | 2 |
| C2×C9×C3⋊C16 | 2 |
| #11720232 | 2 |
| C2×#63546 | 3 |
| C2×D144 | 3 |