Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19149712 | C2 | semidirect |
| 3. #26012062 | C2 | semidirect |
| 4. #26011676 | C2 | semidirect |
| 5. #26011671 | C2 | semidirect |
| 6. #26011507 | C2 | semidirect |
| 7. #413×C173 | C2 | semidirect |
| 16. C22×Dic346 | C22 | semidirect |
| 18. #19149712 | C22 | semidirect |
| 21. #19149677 | C22 | semidirect |
| 22. #19149666 | C22 | semidirect |
| 25. #19149638 | C22 | semidirect |
| 26. #19149605 | C22 | semidirect |
| 28. C2×M16×C173 | C22 | semidirect |
| 29. #101×C173 | C22 | semidirect |
| 30. #100×C173 | C22 | semidirect |
| 129. C173 | #3022 | semidirect |
| 137. #413 | D173 | semidirect |
| 152. C2×M16 | C2×D173 | semidirect |
| 159. #101 | C2×D173 | semidirect |
| 160. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| C2×#19149712 | 2 |
| #26012062 | 2 |
| #26011676 | 2 |
| #26011671 | 2 |
| #26011507 | 2 |
| #413×C173 | 2 |
| #3022 | 173 |