Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 43 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. #22582657 | C3 | semidirect |
| 2. #22582645 | C3 | semidirect |
| 3. #22582602 | C3 | semidirect |
| 4. #22582525 | C3 | semidirect |
| 5. #22582512 | C3 | semidirect |
| 6. #22582503 | C3 | semidirect |
| 7. C37×#6879 | C3 | semidirect |
| 12. #15688521 | C32 | semidirect |
| 18. #15688505 | C32 | semidirect |
| 20. C37×#732 | C32 | semidirect |
| 21. C92×C37 | C32 | semidirect |
| 55. #6879 | C37⋊C3 | semidirect |
| 71. #732 | C3×C37⋊C3 | semidirect |
| 76. C92 | C3×C37⋊C3 | semidirect |
| 77. C37 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582657 | 3 |
| #22582645 | 3 |
| #22582602 | 3 |
| #22582525 | 3 |
| #22582512 | 3 |
| #22582503 | 3 |
| C37×#6879 | 3 |
| #10624851 | 37 |