Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22582575 | C3 | semidirect |
| 2. #22582573 | C3 | semidirect |
| 4. C37⋊#6862 | C3 | semidirect |
| 6. #22582449 | C3 | semidirect |
| 7. #22582449 | C3 | semidirect |
| 9. C37×#6861 | C3 | semidirect |
| 62. #6861 | C37⋊C3 | semidirect |
| 88. C37 | #10624676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582575 | 3 |
| #22582573 | 3 |
| #22582561 | 3 |
| C37⋊#6862 | 3 |
| #22582452 | 3 |
| #22582449 | 3 |
| #22582446 | 3 |
| C37×#6861 | 3 |
| #10624676 | 37 |