Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
680 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 148 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. C33×#66524 | C3 | semidirect |
| 3. C3×C32⋊#66524 | C3 | semidirect |
| 4. #22582475 | C3 | direct (N × H) |
| 5. C3×C37×C32⋊C9 | C3 | semidirect |
| 10. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 16. C32×#66524 | C32 | semidirect |
| 18. C32⋊#66524 | C32 | semidirect |
| 22. C37×C32⋊C9 | C32 | semidirect |
| 42. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 79. C3×C32⋊C9 | C37⋊C3 | semidirect |
| 85. C3×C37 | H(3,𝔽3)⋊C9 | semidirect |
| 107. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 108. C37 | C3×H(3,𝔽3)⋊C9 | semidirect |
| 166. C3 | #22582475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| C33×#66524 | 3 |
| C3×C32⋊#66524 | 3 |
| #22582475 | 3 |
| C3×C37×C32⋊C9 | 3 |
| C3×H(3,𝔽3)⋊C9 | 37 |