Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C27⋊C3×C37⋊C3 | C3 | semidirect |
| 3. #22582474 | C3 | semidirect |
| 4. #22582473 | C3 | semidirect |
| 5. C37×#6869 | C3 | semidirect |
| 18. #15688511 | C32 | semidirect |
| 23. C37×C27⋊C3 | C32 | semidirect |
| 80. #6869 | C37⋊C3 | direct (N × H) |
| 87. C37⋊C3 | #6869 | direct (N × H) |
| 104. C27⋊C3 | C3×C37⋊C3 | semidirect |
| 106. C37 | C3×#6869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| #22582474 | 3 |
| #22582473 | 3 |
| C37×#6869 | 3 |
| C3×#6869 | 37 |