Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012201 | C2 | semidirect |
| 3. #26011837 | C2 | semidirect |
| 4. #26011808 | C2 | semidirect |
| 5. #26011782 | C2 | semidirect |
| 6. #26011717 | C2 | semidirect |
| 7. #26011640 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #102×D173 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 15. C2×C8×D173 | C22 | semidirect |
| 16. #19149679 | C22 | semidirect |
| 19. #19149655 | C22 | semidirect |
| 26. C4⋊C4×D173 | C22 | semidirect |
| 27. #19149611 | C22 | semidirect |
| 28. #19149610 | C22 | semidirect |
| 29. #19149603 | C22 | semidirect |
| 31. #19149600 | C22 | semidirect |
| 32. #19149600 | C22 | semidirect |
| 34. #19149591 | C22 | semidirect |
| 35. C4×#13063436 | C22 | semidirect |
| 36. C2×SD16×C173 | C22 | semidirect |
| 38. C4×Q8×C173 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 84. D692 | SD16 | semidirect |
| 136. C173 | #3295 | semidirect |
| 144. #460 | D173 | semidirect |
| 152. C2×SD16 | C2×D173 | semidirect |
| 162. C4×Q8 | C2×D173 | semidirect |
| 169. C4⋊C8 | C2×D173 | semidirect |
| 175. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| #26012126 | 2 |
| #26011837 | 2 |
| #26011808 | 2 |
| #26011782 | 2 |
| #26011717 | 2 |
| #26011640 | 2 |
| C4×#14583813 | 2 |
| #26011556 | 2 |
| #102×D173 | 2 |
| #460×C173 | 2 |
| #3295 | 173 |