Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
236 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 49 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. #733×C37⋊C3 | C3 | semidirect |
| 3. C92×C37⋊C3 | C3 | semidirect |
| 4. #22582505 | C3 | semidirect |
| 5. #22582504 | C3 | semidirect |
| 6. #22582503 | C3 | semidirect |
| 7. #22582502 | C3 | semidirect |
| 8. #22582501 | C3 | semidirect |
| 9. C37×#6878 | C3 | semidirect |
| 14. #15688521 | C32 | semidirect |
| 15. #15688521 | C32 | semidirect |
| 21. C9×#66524 | C32 | semidirect |
| 22. C37×#733 | C32 | semidirect |
| 24. C92×C37 | C32 | semidirect |
| 68. #6878 | C37⋊C3 | direct (N × H) |
| 75. C37⋊C3 | #6878 | direct (N × H) |
| 83. #733 | C3×C37⋊C3 | semidirect |
| 90. C92 | C3×C37⋊C3 | semidirect |
| 91. C37 | C3×#6878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C37⋊C3 | 3 |
| #732×C37⋊C3 | 3 |
| C92×C37⋊C3 | 3 |
| #22582505 | 3 |
| #22582504 | 3 |
| #22582503 | 3 |
| #22582502 | 3 |
| #22582501 | 3 |
| C37×#6878 | 3 |
| C3×#6878 | 37 |