Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
236 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×#15688521 | C3 | semidirect |
| 3. C3×C9×#66524 | C3 | semidirect |
| 4. #22582504 | C3 | direct (N × H) |
| 5. C3×C37×#733 | C3 | semidirect |
| 10. #15688521 | C32 | semidirect |
| 14. C9×#66524 | C32 | semidirect |
| 18. C37×#733 | C32 | semidirect |
| 48. C3×#733 | C37⋊C3 | semidirect |
| 54. C3×C37 | #6878 | semidirect |
| 65. #733 | C3×C37⋊C3 | semidirect |
| 70. C37 | C3×#6878 | semidirect |
| 101. C3 | #22582504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688521 | 3 |
| C3×#15688519 | 3 |
| C3×C9×#66524 | 3 |
| #22582504 | 3 |
| C3×C37×#733 | 3 |
| C3×#6878 | 37 |