Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
212 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #22582712 | C3 | semidirect |
| 4. #22582710 | C3 | semidirect |
| 5. #22582708 | C3 | semidirect |
| 17. #15688511 | C9 | semidirect |
| 18. #15688510 | C9 | semidirect |
| 20. C27×C37⋊C3 | C9 | semidirect |
| 21. C37×C27⋊C3 | C9 | semidirect |
| 36. C27×C37 | C3×C9 | semidirect |
| 37. #11758601 | C3×C9 | semidirect |
| 62. C37⋊C3 | #6875 | semidirect |
| 71. C27⋊C3 | #66526 | semidirect |
| 78. C37 | C3×#6875 | semidirect |
| 94. C27 | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C37⋊C3)⋊(C27⋊C3) | 3 |
| C3×#15688538 | 3 |
| #22582712 | 3 |
| #22582710 | 3 |
| #22582708 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| C3×#6875 | 37 |