Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1130 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 297 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. C22×C9×C3⋊C8 | C2 | semidirect |
| 3. C22×C3×C9⋊C8 | C2 | semidirect |
| 4. C2×#88414 | C2 | direct (N × H) |
| 12. C2×C9×C3⋊C8 | C22 | semidirect |
| 13. C2×C3×C9⋊C8 | C22 | semidirect |
| 14. #88414 | C22 | direct (N × H) |
| 22. C22×C9⋊C8 | D3 | semidirect |
| 32. C9×C3⋊C8 | C23 | semidirect |
| 33. C3×C9⋊C8 | C23 | semidirect |
| 55. C2×C9⋊C8 | C2×D3 | semidirect |
| 57. C22×C3×C9 | M16 | semidirect |
| 70. C22×C3⋊C8 | D9 | semidirect |
| 100. C9⋊C8 | C22×D3 | semidirect |
| 102. C2×C3×C9 | C2×M16 | semidirect |
| 123. C2×C3⋊C8 | C2×D9 | semidirect |
| 135. C22×C9 | ΓL(1,𝔽25) | semidirect |
| 151. C3×C9 | C22×M16 | semidirect |
| 179. C3⋊C8 | C22×D9 | semidirect |
| 185. C2×C9 | C2×ΓL(1,𝔽25) | semidirect |
| 199. C22×C3 | #3663 | semidirect |
| 220. C9 | C22×ΓL(1,𝔽25) | semidirect |
| 233. C2×C3 | C2×#3663 | semidirect |
| 242. C22 | #88414 | direct (N × H) |
| 248. C3 | C22×#3663 | semidirect |
| 251. C2 | C2×#88414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D9 | 2 |
| C22×C9×C3⋊C8 | 2 |
| C22×C3×C9⋊C8 | 2 |
| C2×#88414 | 2 |
| C22×#3712 | 3 |
| C22×#3663 | 3 |