Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
224 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 224 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 |
| 2. C3×#15688519 | C3 | semidirect |
| 3. C3×#15688505 | C3 | semidirect |
| 4. #22582512 | C3 | direct (N × H) |
| 5. C3×C37×#732 | C3 | semidirect |
| 10. #15688521 | C32 | semidirect |
| 12. #15688519 | C32 | semidirect |
| 14. #15688505 | C32 | semidirect |
| 18. C37×#732 | C32 | semidirect |
| 50. C3×#732 | C37⋊C3 | semidirect |
| 56. C3×C37 | #6881 | semidirect |
| 69. #732 | C3×C37⋊C3 | semidirect |
| 72. C37 | C3×#6881 | semidirect |
| 105. C3 | #22582512 | 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×#15688505 | 3 |
| #22582512 | 3 |
| C3×C37×#732 | 3 |
| C3×#6881 | 37 |