Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #26012046 | C2 | semidirect |
| 3. #26011854 | C2 | semidirect |
| 4. #26011839 | C2 | semidirect |
| 5. #26011838 | C2 | semidirect |
| 6. #26011837 | C2 | semidirect |
| 7. #26011494 | C2 | semidirect |
| 8. C4×#14583809 | C2 | semidirect |
| 9. #486×C173 | C2 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 19. #19149670 | C22 | semidirect |
| 26. #19149601 | C22 | semidirect |
| 27. #19149600 | C22 | semidirect |
| 28. #19149599 | C22 | semidirect |
| 29. #19149589 | C22 | semidirect |
| 30. C4×#13063436 | C22 | semidirect |
| 31. C4⋊Q8×C173 | C22 | semidirect |
| 33. #102×C173 | C22 | semidirect |
| 34. C4×C8×C173 | C22 | semidirect |
| 123. C173 | #3138 | semidirect |
| 131. #486 | D173 | semidirect |
| 139. C4⋊Q8 | C2×D173 | semidirect |
| 155. #102 | C2×D173 | semidirect |
| 158. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #127×D173 | 2 |
| #26011854 | 2 |
| #26011839 | 2 |
| #26011838 | 2 |
| #26011837 | 2 |
| #26011494 | 2 |
| C4×#14583809 | 2 |
| #486×C173 | 2 |
| #3138 | 173 |