Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. #26011819 | C2 | semidirect |
| 3. #26011809 | C2 | semidirect |
| 4. #26011722 | C2 | semidirect |
| 5. #26011641 | C2 | semidirect |
| 6. #26011630 | C2 | semidirect |
| 7. C2×C22⋊#13063436 | C2 | semidirect |
| 8. C2×C22⋊Q8×C173 | C2 | semidirect |
| 11. C2×#14583813 | C22 | semidirect |
| 12. C22×#13063436 | C22 | semidirect |
| 19. #19149610 | C22 | semidirect |
| 20. #19149603 | C22 | semidirect |
| 21. #19149599 | C22 | semidirect |
| 23. C22⋊#13063436 | C22 | semidirect |
| 24. C22×Q8×C173 | C22 | semidirect |
| 29. C22⋊Q8×C173 | C22 | semidirect |
| 31. C2×C4⋊C4×C173 | C22 | semidirect |
| 80. C23×C173 | SD16 | semidirect |
| 129. C173 | #3187 | semidirect |
| 131. C2×C22⋊Q8 | D173 | semidirect |
| 139. C22×Q8 | C2×D173 | semidirect |
| 148. C22⋊Q8 | C2×D173 | semidirect |
| 155. C2×C4⋊C4 | C2×D173 | semidirect |
| 203. C23 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011819 | 2 |
| #26011809 | 2 |
| #26011722 | 2 |
| #26011641 | 2 |
| #26011630 | 2 |
| C2×C22⋊#13063436 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #3187 | 173 |