Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
226 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 52 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. #22582633 | C3 | semidirect |
| 2. #22582510 | C3 | semidirect |
| 3. #22582507 | C3 | semidirect |
| 4. #22582503 | C3 | semidirect |
| 5. #22582502 | C3 | semidirect |
| 6. C3×C92×C37 | C3 | semidirect |
| 50. C3×C92 | C37⋊C3 | semidirect |
| 71. C37 | #10624837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582633 | 3 |
| #22582510 | 3 |
| #22582507 | 3 |
| #22582503 | 3 |
| #22582502 | 3 |
| C3×C92×C37 | 3 |
| #10624837 | 37 |