Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. C2×#19149658 | C2 | semidirect |
| 3. #26011827 | C2 | semidirect |
| 4. #26011805 | C2 | semidirect |
| 5. #26011737 | C2 | semidirect |
| 6. #26011644 | C2 | semidirect |
| 7. #26011632 | C2 | semidirect |
| 8. #407×C173 | C2 | semidirect |
| 9. C22×Dic346 | C22 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 16. #19149658 | C22 | semidirect |
| 22. C2×C4⋊Dic173 | C22 | semidirect |
| 26. #19149613 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 30. C2×M16×C173 | C22 | semidirect |
| 32. C22⋊C8×C173 | C22 | semidirect |
| 129. C173 | #3193 | semidirect |
| 138. #407 | D173 | semidirect |
| 144. C2×M16 | C2×D173 | semidirect |
| 162. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| C2×#19149653 | 2 |
| #26011827 | 2 |
| #26011805 | 2 |
| #26011737 | 2 |
| #26011644 | 2 |
| #26011632 | 2 |
| #407×C173 | 2 |
| #3193 | 173 |