Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#19149638 | C2 | semidirect |
| 3. #26011816 | C2 | direct (N × H) |
| 4. C2×#19149613 | C2 | semidirect |
| 5. C2×#19149611 | C2 | semidirect |
| 6. C2×#19149601 | C2 | semidirect |
| 7. C2×#19149601 | C2 | semidirect |
| 8. C2×C22⋊C8×C173 | C2 | semidirect |
| 14. #19149638 | C22 | semidirect |
| 21. #19149613 | C22 | semidirect |
| 22. #19149611 | C22 | semidirect |
| 23. #19149601 | C22 | semidirect |
| 24. #19149601 | C22 | semidirect |
| 28. C22⋊C8×C173 | C22 | semidirect |
| 109. C2×C173 | #482 | semidirect |
| 114. C173 | C2×#482 | semidirect |
| 123. C2×C22⋊C8 | D173 | semidirect |
| 143. C22⋊C8 | C2×D173 | semidirect |
| 225. C2 | #26011816 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| C2×#19149638 | 2 |
| #26011816 | 2 |
| C2×#19149613 | 2 |
| C2×#19149611 | 2 |
| C2×#19149601 | 2 |
| C2×C22⋊C8×C173 | 2 |
| C2×#482 | 173 |