Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #26012144 | C2 | semidirect |
| 2. #26012126 | C2 | semidirect |
| 3. #26011803 | C2 | semidirect |
| 4. #26011768 | C2 | semidirect |
| 5. #26011726 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011626 | C2 | semidirect |
| 8. C4×D1384 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #102×D173 | C2 | semidirect |
| 11. #486×C173 | C2 | semidirect |
| 16. C2×#14583811 | C22 | semidirect |
| 17. C2×C8×D173 | C22 | semidirect |
| 20. #19149654 | C22 | semidirect |
| 26. C4×D692 | C22 | semidirect |
| 27. C4⋊C4×D173 | C22 | semidirect |
| 28. #19149613 | C22 | semidirect |
| 29. #19149612 | C22 | semidirect |
| 30. C4⋊#13063436 | C22 | semidirect |
| 32. #19149601 | C22 | semidirect |
| 33. #19149600 | C22 | semidirect |
| 35. #19149591 | C22 | semidirect |
| 36. C4⋊Q8×C173 | C22 | semidirect |
| 38. #102×C173 | C22 | semidirect |
| 39. #102×C173 | C22 | semidirect |
| 40. C4×C8×C173 | C22 | semidirect |
| 88. D692 | D8 | semidirect |
| 89. D692 | #41 | semidirect |
| 142. C173 | #3294 | semidirect |
| 146. #486 | D173 | semidirect |
| 161. C4⋊Q8 | C2×D173 | semidirect |
| 180. #102 | C2×D173 | semidirect |
| 181. #102 | C2×D173 | semidirect |
| 183. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012144 | 2 |
| #26012126 | 2 |
| #26011803 | 2 |
| #26011768 | 2 |
| #26011726 | 2 |
| #26011683 | 2 |
| #26011626 | 2 |
| C4×D1384 | 2 |
| C8×D692 | 2 |
| #102×D173 | 2 |
| #486×C173 | 2 |
| #3294 | 173 |