Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14583813 | C2 | semidirect |
| 2. C22×#14583810 | C2 | semidirect |
| 4. #26011739 | C2 | direct (N × H) |
| 5. C2×#19149612 | C2 | semidirect |
| 6. C2×#19149603 | C2 | semidirect |
| 7. C2×#19149599 | C2 | semidirect |
| 8. C2×C22⋊Q8×C173 | C2 | semidirect |
| 12. C2×#14583813 | C22 | semidirect |
| 14. C2×#14583810 | C22 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149603 | C22 | semidirect |
| 23. #19149599 | C22 | semidirect |
| 27. C22⋊Q8×C173 | C22 | semidirect |
| 42. C2×#13063436 | D4 | semidirect |
| 76. #13063436 | C2×D4 | semidirect |
| 118. C2×C173 | #468 | semidirect |
| 123. C173 | C2×#468 | semidirect |
| 127. C2×C22⋊Q8 | D173 | semidirect |
| 144. C22⋊Q8 | C2×D173 | semidirect |
| 243. C2 | #26011739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583813 | 2 |
| C22×#14583810 | 2 |
| C2×#19149653 | 2 |
| #26011739 | 2 |
| C2×#19149612 | 2 |
| C2×#19149603 | 2 |
| C2×#19149599 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| C2×#468 | 173 |