Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
566 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 2. C3×#15688517 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. C3×C32⋊#66524 | C3 | semidirect |
| 5. C37×#6891 | C3 | semidirect |
| 7. C3×#11758608 | C32 | semidirect |
| 11. C32×#66524 | C32 | semidirect |
| 18. C3×3−1+2×C37 | C32 | semidirect |
| 49. C32×C37 | #731 | semidirect |
| 62. #6891 | C37⋊C3 | semidirect |
| 74. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 86. C37 | #10624741 | semidirect |
| 118. C32 | #15688517 | 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×#15688517 | 3 |
| #22582554 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×#6891 | 3 |
| #10624741 | 37 |