Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
190 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 43 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. #22582658 | C3 | semidirect |
| 2. #22582646 | C3 | semidirect |
| 3. #22582595 | C3 | semidirect |
| 4. #22582524 | C3 | semidirect |
| 5. #22582511 | C3 | semidirect |
| 6. #22582502 | C3 | semidirect |
| 7. C37×#6879 | C3 | semidirect |
| 11. #15688521 | C32 | semidirect |
| 16. #15688506 | C32 | semidirect |
| 20. C37×#732 | C32 | semidirect |
| 21. C92×C37 | C32 | semidirect |
| 54. #6879 | C37⋊C3 | semidirect |
| 69. #732 | C3×C37⋊C3 | semidirect |
| 75. C92 | C3×C37⋊C3 | semidirect |
| 76. C37 | #10624853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582658 | 3 |
| #22582646 | 3 |
| #22582595 | 3 |
| #22582524 | 3 |
| #22582511 | 3 |
| #22582502 | 3 |
| C37×#6879 | 3 |
| #10624853 | 37 |