Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
770 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 73 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×C32⋊(C37⋊C3) | C3 | semidirect |
| 2. C3×#15688513 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. C32×H(3,𝔽3)×C37 | C3 | semidirect |
| 6. C3×#11758608 | C32 | semidirect |
| 14. C34×C37 | C32 | semidirect |
| 36. C32⋊(C37⋊C3) | H(3,𝔽3) | semidirect |
| 52. C32×C37 | AΣL(1,𝔽27) | semidirect |
| 61. C32×H(3,𝔽3) | C37⋊C3 | semidirect |
| 74. C34 | C3×C37⋊C3 | semidirect |
| 85. C37 | #10624742 | semidirect |
| 123. C32 | #15688513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| C3×#15688513 | 3 |
| #22582554 | 3 |
| C32×H(3,𝔽3)×C37 | 3 |
| #10624742 | 37 |