Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1259 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1259 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 2. C22×#6180 | C2 | semidirect |
| 3. C2×#88432 | C2 | direct (N × H) |
| 8. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 9. C2×#6180 | C22 | semidirect |
| 10. #88432 | C22 | direct (N × H) |
| 11. C22×C4⋊(C3⋊D3) | D3 | semidirect |
| 22. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 23. #6180 | C23 | semidirect |
| 31. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 37. C22×H(3,𝔽3) | D8 | semidirect |
| 62. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 68. C2×H(3,𝔽3) | C2×D8 | semidirect |
| 90. C22×C32 | #213 | semidirect |
| 103. H(3,𝔽3) | C22×D8 | semidirect |
| 130. C2×C32 | C2×#213 | semidirect |
| 159. C32 | C22×#213 | semidirect |
| 179. C22 | #88432 | direct (N × H) |
| 187. C2 | C2×#88432 | 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⋊D3)⋊C3) | 2 |
| C22×#6180 | 2 |
| C2×#88432 | 2 |
| C22×#3714 | 3 |