Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
144 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 39 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. C32×#11758603 | C3 | semidirect |
| 2. C32⋊#11758603 | C3 | semidirect |
| 18. C32⋊(C37⋊C3) | C27 | semidirect |
| 68. C37 | H(3,𝔽3)⋊C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758603 | 3 |
| C32⋊#11758603 | 3 |
| #22582539 | 3 |
| H(3,𝔽3)⋊C27 | 37 |