Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19149703 | C2 | semidirect |
| 2. #26012136 | C2 | semidirect |
| 3. #26011875 | C2 | semidirect |
| 4. #26011738 | C2 | semidirect |
| 5. #26011706 | C2 | semidirect |
| 6. #26011654 | C2 | semidirect |
| 7. #26011626 | C2 | semidirect |
| 8. #26011570 | C2 | semidirect |
| 9. C4×D8×C173 | C2 | semidirect |
| 11. C2×D4×D173 | C22 | semidirect |
| 13. C2×Dic692 | C22 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 18. C2×#14583809 | C22 | semidirect |
| 19. #19149667 | C22 | semidirect |
| 21. #19149659 | C22 | semidirect |
| 27. C4⋊#13063436 | C22 | semidirect |
| 28. #19149602 | C22 | semidirect |
| 29. #19149599 | C22 | semidirect |
| 30. #19149591 | C22 | semidirect |
| 32. C4×D4×C173 | C22 | semidirect |
| 33. #107×C173 | C22 | semidirect |
| 34. #102×C173 | C22 | semidirect |
| 35. C4×C8×C173 | C22 | semidirect |
| 65. D8×C173 | D4 | semidirect |
| 124. C173 | #3273 | semidirect |
| 133. C4×D8 | D173 | semidirect |
| 152. C4×D4 | C2×D173 | semidirect |
| 154. #107 | C2×D173 | semidirect |
| 158. #102 | C2×D173 | semidirect |
| 160. C4×C8 | C2×D173 | semidirect |
| 181. D8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149703 | 2 |
| #26012136 | 2 |
| #26011875 | 2 |
| #26011738 | 2 |
| #26011706 | 2 |
| #26011654 | 2 |
| #26011626 | 2 |
| #26011570 | 2 |
| C4×D8×C173 | 2 |
| #3273 | 173 |