Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 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. #26012045 | C2 | semidirect |
| 3. #26011862 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011691 | C2 | semidirect |
| 7. #26011688 | C2 | semidirect |
| 8. #26011643 | C2 | semidirect |
| 9. #26011640 | C2 | semidirect |
| 10. #26011543 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 17. C2×#14583813 | C22 | semidirect |
| 18. #19149678 | C22 | semidirect |
| 19. #19149677 | C22 | semidirect |
| 29. C4×Dic346 | C22 | semidirect |
| 32. C4⋊#13063436 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 38. C2×SD16×C173 | C22 | semidirect |
| 40. C4×Q8×C173 | C22 | semidirect |
| 41. C4⋊C8×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 109. C4×D173 | SD16 | semidirect |
| 152. C173 | #3208 | semidirect |
| 161. #460 | D173 | semidirect |
| 171. C2×SD16 | C2×D173 | semidirect |
| 185. C4×Q8 | C2×D173 | semidirect |
| 189. C4⋊C8 | C2×D173 | semidirect |
| 193. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012045 | 2 |
| #127×D173 | 2 |
| #26011862 | 2 |
| #26011836 | 2 |
| #26011692 | 2 |
| #26011691 | 2 |
| #26011688 | 2 |
| #26011643 | 2 |
| #26011640 | 2 |
| #26011543 | 2 |
| #460×C173 | 2 |
| #3208 | 173 |