Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149724 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011633 | C2 | semidirect |
| 5. #26011623 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. #26011457 | C2 | semidirect |
| 9. C22×D8×C173 | C2 | semidirect |
| 15. C2×#14583825 | C22 | semidirect |
| 18. C2×D4×D173 | C22 | semidirect |
| 20. C2×#14583814 | C22 | semidirect |
| 21. C2×#14583811 | C22 | semidirect |
| 22. C2×#14583810 | C22 | semidirect |
| 25. #19149650 | C22 | semidirect |
| 27. #19149638 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 30. #19149600 | C22 | semidirect |
| 31. #19149591 | C22 | semidirect |
| 33. C22×D4×C173 | C22 | semidirect |
| 35. C2×D8×C173 | C22 | semidirect |
| 36. C22×C8×C173 | C22 | semidirect |
| 41. #14583826 | D4 | semidirect |
| 76. C2×D4×C173 | D4 | semidirect |
| 151. C173 | #3008 | semidirect |
| 155. C22×D8 | D173 | semidirect |
| 172. C22×D4 | C2×D173 | semidirect |
| 177. C2×D8 | C2×D173 | semidirect |
| 179. C22×C8 | C2×D173 | semidirect |
| 217. C2×D4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149705 | 2 |
| #26012058 | 2 |
| #26011633 | 2 |
| #26011623 | 2 |
| #26011496 | 2 |
| #26011488 | 2 |
| #26011457 | 2 |
| C22×D8×C173 | 2 |
| #3008 | 173 |