Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
274 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 17. #15688521 | C9 | semidirect |
| 18. #15688520 | C9 | semidirect |
| 19. C37×#733 | C9 | semidirect |
| 49. #66526 | #733 | direct (N × H) |
| 71. #733 | #66526 | direct (N × H) |
| 79. C37 | C9×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#66526 | 3 |
| C3×C9×#66526 | 3 |
| 3−1+2⋊#66526 | 3 |
| #22582693 | 3 |
| #733×C37⋊C3 | 3 |
| C9×#733 | 37 |