Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149710 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. #26012041 | C2 | semidirect |
| 4. #26011886 | C2 | semidirect |
| 5. #26011881 | C2 | semidirect |
| 6. #26011873 | C2 | semidirect |
| 7. C4×#14583810 | C2 | semidirect |
| 8. C2×#124×C173 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 17. #19149679 | C22 | semidirect |
| 18. #19149676 | C22 | semidirect |
| 19. #19149667 | C22 | semidirect |
| 22. #19149590 | C22 | semidirect |
| 23. C4×#13063436 | C22 | semidirect |
| 42. #14583810 | D4 | semidirect |
| 106. C173 | #3153 | semidirect |
| 111. C2×#124 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| C2×#19149705 | 2 |
| #26012041 | 2 |
| #26011886 | 2 |
| #26011881 | 2 |
| #26011873 | 2 |
| C4×#14583810 | 2 |
| C2×#124×C173 | 2 |
| #3153 | 173 |