Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#19149699 | C2 | semidirect |
| 2. #26012058 | C2 | semidirect |
| 3. #26011974 | C2 | semidirect |
| 4. #26011711 | C2 | semidirect |
| 5. #26011704 | C2 | semidirect |
| 6. #26011689 | C2 | semidirect |
| 7. #26011684 | C2 | semidirect |
| 8. #26011519 | C2 | semidirect |
| 9. #26011493 | C2 | semidirect |
| 10. C2×#19149600 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 14. C2×#14583816 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 24. Q8×Dic173 | C22 | semidirect |
| 26. D4×Dic173 | C22 | semidirect |
| 31. #19149608 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 73. #41×C173 | D4 | semidirect |
| 154. C173 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 202. #41 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| #26012058 | 2 |
| #26011974 | 2 |
| #26011711 | 2 |
| #26011704 | 2 |
| #26011689 | 2 |
| #26011684 | 2 |
| #26011519 | 2 |
| #26011493 | 2 |
| C2×#19149600 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3045 | 173 |