Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
5860 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 5860 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88907 | C2 | direct (N × H) |
| 3. C22×C22⋊(C22⋊C9) | C3 | semidirect |
| 4. #88907 | C22 | direct (N × H) |
| 9. C2×C22⋊(C22⋊C9) | C2×C3 | semidirect |
| 22. C22⋊(C22⋊C9) | C22×C3 | semidirect |
| 43. C26 | 3−1+2 | semidirect |
| 76. C25 | C2×3−1+2 | semidirect |
| 109. C24 | #1094 | semidirect |
| 110. C24 | C22×3−1+2 | semidirect |
| 140. C23 | C2×#1094 | semidirect |
| 154. C22 | C22×#1094 | semidirect |
| 155. C22 | #88907 | direct (N × H) |
| 160. C2 | C2×#88907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88907 | 2 |
| C26×C32 | 3 |
| C22×C22⋊(C22⋊C9) | 3 |
| C22×#1094 | 4 |