Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
541 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 541 conjugacy classes of subgroups — too many to draw. Only its 147 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×#6180 | C2 | semidirect |
| 4. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 5. #11720312 | C2 | semidirect |
| 15. #88430 | C4 | direct (N × H) |
| 20. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 34. #6180 | C2×C4 | semidirect |
| 35. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 60. C4×H(3,𝔽3) | M16 | semidirect |
| 96. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 140. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 141. C32×C4 | #208 | semidirect |
| 153. H(3,𝔽3) | C4×M16 | semidirect |
| 225. C32 | C4×ΓL(1,𝔽25) | semidirect |
| 226. C32 | C4×#208 | semidirect |
| 252. C4 | #88430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×(C3⋊D3)⋊C3 | 2 |
| C2×#88430 | 2 |
| C4×#6180 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #11720312 | 2 |
| C4×#3712 | 3 |
| C4×#3711 | 3 |