Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
220 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 220 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. #22582548 | C3 | semidirect |
| 3. #22582535 | C3 | semidirect |
| 4. #22582457 | C3 | semidirect |
| 6. #22582450 | C3 | semidirect |
| 7. #22582448 | C3 | semidirect |
| 9. C37×#6862 | C3 | semidirect |
| 60. #6862 | C37⋊C3 | semidirect |
| 86. C37 | #10624587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582548 | 3 |
| #22582539 | 3 |
| #22582535 | 3 |
| #22582457 | 3 |
| #22582453 | 3 |
| #22582450 | 3 |
| #22582448 | 3 |
| #22582446 | 3 |
| C37×#6862 | 3 |
| #10624587 | 37 |