Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
320 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 320 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. C3×C27×C37⋊C3 | C3 | semidirect |
| 4. #22582484 | C3 | semidirect |
| 5. #22582483 | C3 | semidirect |
| 6. #22582482 | C3 | semidirect |
| 7. C37×#6872 | C3 | semidirect |
| 18. #15688511 | C32 | semidirect |
| 21. C3×#11758601 | C32 | semidirect |
| 26. C37×C27⋊C3 | C32 | semidirect |
| 27. C3×C27×C37 | C32 | semidirect |
| 78. #6872 | C37⋊C3 | direct (N × H) |
| 84. C37⋊C3 | #6872 | direct (N × H) |
| 99. C27⋊C3 | C3×C37⋊C3 | semidirect |
| 104. C3×C27 | C3×C37⋊C3 | semidirect |
| 105. C37 | C3×#6872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C37⋊C3 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| C3×C27×C37⋊C3 | 3 |
| #22582484 | 3 |
| #22582483 | 3 |
| #22582482 | 3 |
| C37×#6872 | 3 |
| C3×#6872 | 37 |