Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
534 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C4×C9×C3⋊C8 | C2 | semidirect |
| 4. C3×C4×C9⋊C8 | C2 | semidirect |
| 5. #11720275 | C2 | semidirect |
| 15. #88414 | C4 | direct (N × H) |
| 26. C4×C9⋊C8 | D3 | semidirect |
| 34. C9×C3⋊C8 | C2×C4 | semidirect |
| 35. C3×C9⋊C8 | C2×C4 | semidirect |
| 62. C3×C4×C9 | M16 | semidirect |
| 76. C4×C3⋊C8 | D9 | semidirect |
| 101. C9⋊C8 | C4×D3 | semidirect |
| 142. C4×C9 | ΓL(1,𝔽25) | semidirect |
| 153. C3×C9 | C4×M16 | semidirect |
| 178. C3⋊C8 | C4×D9 | semidirect |
| 207. C3×C4 | #3663 | semidirect |
| 219. C9 | C4×ΓL(1,𝔽25) | semidirect |
| 243. C4 | #88414 | direct (N × H) |
| 246. C3 | C4×#3663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊D9 | 2 |
| C2×#88414 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #11720275 | 2 |
| C4×#3712 | 3 |
| C4×#3663 | 3 |