Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19149705 | C2 | semidirect |
| 2. #26012041 | C2 | semidirect |
| 3. #26011706 | C2 | semidirect |
| 4. #26011696 | C2 | semidirect |
| 5. #26011686 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 7. #26011490 | C2 | semidirect |
| 8. C2×C4×D4×C173 | C2 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 15. #19149676 | C22 | semidirect |
| 16. #19149667 | C22 | semidirect |
| 21. C4⋊#13063436 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149602 | C22 | semidirect |
| 24. #19149599 | C22 | semidirect |
| 53. C2×D4×C173 | D4 | semidirect |
| 119. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 129. C173 | #3036 | semidirect |
| 133. C2×C4×D4 | D173 | semidirect |
| 174. C2×D4 | D692 | semidirect |
| 250. C4 | #19149705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| #26012041 | 2 |
| #26011706 | 2 |
| #26011696 | 2 |
| #26011686 | 2 |
| #26011515 | 2 |
| #26011490 | 2 |
| C2×C4×D4×C173 | 2 |
| #3036 | 173 |