Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19149653 | C2 | semidirect |
| 2. #26011804 | C2 | semidirect |
| 3. #26011802 | C2 | semidirect |
| 4. #26011725 | C2 | semidirect |
| 5. #26011625 | C2 | semidirect |
| 6. #26011624 | C2 | semidirect |
| 7. C2×C22⋊#13063436 | C2 | semidirect |
| 8. C2×#121×C173 | C2 | semidirect |
| 9. C22×D692 | C22 | semidirect |
| 11. C2×#14583811 | C22 | semidirect |
| 12. C22×#13063436 | C22 | semidirect |
| 16. #19149653 | C22 | semidirect |
| 17. C2×C4⋊Dic173 | C22 | semidirect |
| 19. #19149612 | C22 | semidirect |
| 20. #19149600 | C22 | semidirect |
| 21. #19149599 | C22 | semidirect |
| 22. C22⋊#13063436 | C22 | semidirect |
| 23. C22⋊#13063436 | C22 | semidirect |
| 25. C22×D4×C173 | C22 | semidirect |
| 30. #121×C173 | C22 | semidirect |
| 31. C2×C4⋊C4×C173 | C22 | semidirect |
| 85. C23×C173 | D8 | semidirect |
| 138. C173 | #3186 | semidirect |
| 141. C2×#121 | D173 | semidirect |
| 151. C22×D4 | C2×D173 | semidirect |
| 162. #121 | C2×D173 | semidirect |
| 164. C2×C4⋊C4 | C2×D173 | semidirect |
| 217. C23 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011804 | 2 |
| #26011802 | 2 |
| #26011725 | 2 |
| #26011625 | 2 |
| #26011624 | 2 |
| C2×C22⋊#13063436 | 2 |
| C2×#121×C173 | 2 |
| #3186 | 173 |