Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
344 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22582722 | C3 | semidirect |
| 2. C3×#15688538 | C3 | semidirect |
| 3. 3−1+2⋊#66526 | C3 | semidirect |
| 14. #15688532 | C9 | semidirect |
| 16. #15688531 | C9 | semidirect |
| 17. #15688530 | C9 | semidirect |
| 23. C37×#737 | C9 | semidirect |
| 85. #737 | #66526 | semidirect |
| 98. C37 | #10624700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582722 | 3 |
| C3×#15688538 | 3 |
| 3−1+2⋊#66526 | 3 |
| H(3,𝔽3)⋊#66526 | 3 |
| #737×C37⋊C3 | 3 |
| #10624700 | 37 |