Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1368 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 106 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. #13048167 | C2 | direct (N × H) |
| 3. C2×C22⋊(C22⋊C27) | C3 | semidirect |
| 8. C22⋊(C22⋊C27) | C2×C3 | semidirect |
| 78. C25 | C27⋊C3 | semidirect |
| 102. C24 | C2×C27⋊C3 | semidirect |
| 120. C23 | #66353 | semidirect |
| 131. C22 | C2×#66353 | semidirect |
| 136. C2 | #13048167 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13048167 | 2 |
| C25×C3×C9 | 3 |
| C2×C22⋊(C22⋊C27) | 3 |
| C2×#66353 | 4 |