Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14583814 | C2 | semidirect |
| 2. #26012062 | C2 | semidirect |
| 3. #26011966 | C2 | semidirect |
| 4. #26011704 | C2 | semidirect |
| 5. #26011694 | C2 | semidirect |
| 6. #26011519 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 14. #19149677 | C22 | semidirect |
| 15. #19149666 | C22 | semidirect |
| 23. #19149608 | C22 | semidirect |
| 24. #19149604 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 26. #19149600 | C22 | semidirect |
| 116. C173 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| #26012062 | 2 |
| #26011966 | 2 |
| #26011704 | 2 |
| #26011694 | 2 |
| #26011519 | 2 |
| #26011501 | 2 |
| #26011487 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3042 | 173 |