Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 14. #15688520 | C9 | direct (N × H) |
| 58. C9×C37 | #733 | semidirect |
| 97. C37 | C9×#733 | semidirect |
| 133. C9 | #15688520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688520 | 3 |
| C9×#11758608 | 3 |
| C3×C9×#66524 | 3 |
| #22582481 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| #22582471 | 3 |
| C9×3−1+2×C37 | 3 |
| C9×#733 | 37 |