Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19149705 | C2 | semidirect |
| 2. #26012058 | C2 | semidirect |
| 3. #26011966 | C2 | semidirect |
| 4. #26011704 | C2 | semidirect |
| 5. #26011684 | C2 | semidirect |
| 6. #26011517 | C2 | semidirect |
| 7. #26011496 | C2 | semidirect |
| 8. #26011488 | C2 | semidirect |
| 9. C22×D8×C173 | C2 | semidirect |
| 12. C2×#14583814 | C22 | semidirect |
| 13. C2×#14583811 | C22 | semidirect |
| 15. #19149675 | C22 | semidirect |
| 16. #19149666 | C22 | semidirect |
| 20. D4×Dic173 | C22 | semidirect |
| 24. #19149608 | C22 | semidirect |
| 25. #19149604 | C22 | semidirect |
| 26. #19149601 | C22 | semidirect |
| 27. #19149600 | C22 | semidirect |
| 60. C2×D4×C173 | D4 | semidirect |
| 121. C173 | #3041 | semidirect |
| 124. C22×D8 | D173 | semidirect |
| 168. C2×D4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| #26012058 | 2 |
| #26011966 | 2 |
| #26011704 | 2 |
| #26011684 | 2 |
| #26011517 | 2 |
| #26011496 | 2 |
| #26011488 | 2 |
| C22×D8×C173 | 2 |
| #3041 | 173 |