Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
530 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 67 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. C32×C9×C37⋊C3 | C3 | semidirect |
| 2. C3×#15688520 | C3 | semidirect |
| 3. C3×#15688518 | C3 | semidirect |
| 4. C3×#15688517 | C3 | semidirect |
| 5. C3×#15688515 | C3 | semidirect |
| 6. C3×#15688514 | C3 | semidirect |
| 7. C3×#15688512 | C3 | semidirect |
| 8. #22582564 | C3 | semidirect |
| 9. C37×#6893 | C3 | semidirect |
| 99. #6893 | C37⋊C3 | semidirect |
| 129. C37 | #10624734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C3×#15688520 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C3×#15688514 | 3 |
| C3×#15688512 | 3 |
| #22582564 | 3 |
| C37×#6893 | 3 |
| #10624734 | 37 |