Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. C2×#19149727 | C2 | semidirect |
| 2. #26012291 | C2 | semidirect |
| 3. #26012065 | C2 | semidirect |
| 4. #26011676 | C2 | semidirect |
| 5. #26011666 | C2 | semidirect |
| 6. #26011507 | C2 | semidirect |
| 7. C2×#101×C173 | C2 | semidirect |
| 17. #19149712 | C22 | semidirect |
| 19. #19149707 | C22 | semidirect |
| 21. #19149677 | C22 | semidirect |
| 22. #19149668 | C22 | semidirect |
| 26. #19149605 | C22 | semidirect |
| 29. #101×C173 | C22 | semidirect |
| 123. C173 | #3020 | semidirect |
| 131. C2×#101 | D173 | semidirect |
| 153. #101 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| #26012291 | 2 |
| #26012065 | 2 |
| #26011676 | 2 |
| #26011666 | 2 |
| #26011507 | 2 |
| C2×#101×C173 | 2 |
| #3020 | 173 |