Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 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. #26012119 | C2 | semidirect |
| 2. #26011791 | C2 | semidirect |
| 3. #26011791 | C2 | semidirect |
| 4. #26011781 | C2 | semidirect |
| 5. #26011771 | C2 | semidirect |
| 6. #26011534 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011518 | C2 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 16. #19149671 | C22 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149610 | C22 | semidirect |
| 26. #19149610 | C22 | semidirect |
| 27. C4⋊#13063436 | C22 | semidirect |
| 28. C4⋊#13063436 | C22 | semidirect |
| 60. C2×D4×C173 | Q8 | semidirect |
| 124. C173 | #3081 | semidirect |
| 170. C2×D4 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011791 | 2 |
| #26011781 | 2 |
| #26011771 | 2 |
| #26011534 | 2 |
| #26011527 | 2 |
| #26011518 | 2 |
| #26011496 | 2 |
| C2×#19149600 | 2 |
| #518×C173 | 2 |
| #3081 | 173 |