Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012144 | C2 | semidirect |
| 2. D4×D692 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011806 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011687 | C2 | semidirect |
| 7. #26011626 | C2 | semidirect |
| 8. C4×#14583811 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #102×D173 | C2 | semidirect |
| 11. #474×C173 | C2 | semidirect |
| 15. C2×D1384 | C22 | semidirect |
| 17. C2×C8×D173 | C22 | semidirect |
| 22. #19149654 | C22 | semidirect |
| 26. C4×D692 | C22 | semidirect |
| 27. C4⋊C4×D173 | C22 | semidirect |
| 28. #19149612 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 31. #19149599 | C22 | semidirect |
| 32. #19149599 | C22 | semidirect |
| 33. #19149599 | C22 | semidirect |
| 34. #19149591 | C22 | semidirect |
| 35. C4×#13063436 | C22 | semidirect |
| 36. C4⋊Q8×C173 | C22 | semidirect |
| 38. #107×C173 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 92. D692 | D8 | semidirect |
| 105. D4×C173 | #41 | semidirect |
| 142. C173 | #3294 | semidirect |
| 148. #474 | D173 | semidirect |
| 161. C4⋊Q8 | C2×D173 | semidirect |
| 174. #107 | C2×D173 | semidirect |
| 175. C4⋊C8 | C2×D173 | semidirect |
| 240. D4 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012144 | 2 |
| D4×D692 | 2 |
| #26011839 | 2 |
| #26011806 | 2 |
| #26011728 | 2 |
| #26011687 | 2 |
| #26011626 | 2 |
| C4×#14583811 | 2 |
| #26011556 | 2 |
| #102×D173 | 2 |
| #474×C173 | 2 |
| #3294 | 173 |