Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2072 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#15688513 | C3 | semidirect |
| 2. #22582554 | C3 | semidirect |
| 3. #22582550 | C3 | semidirect |
| 4. C35×C37 | C3 | semidirect |
| 5. C3×#11758608 | C32 | semidirect |
| 7. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 25. C33×C37 | H(3,𝔽3) | semidirect |
| 42. C32×C37 | AΣL(1,𝔽27) | semidirect |
| 48. C35 | C37⋊C3 | semidirect |
| 68. C37 | #10624730 | semidirect |
| 80. C33 | C32⋊(C37⋊C3) | semidirect |
| 97. C32 | #15688513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688513 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C35×C37 | 3 |
| #10624730 | 37 |