Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26011878 | C2 | semidirect |
| 4. #26011867 | C2 | semidirect |
| 5. #26011863 | C2 | semidirect |
| 6. C4×#14583810 | C2 | semidirect |
| 7. C2×#127×C173 | C2 | semidirect |
| 10. C2×#14583814 | C22 | semidirect |
| 11. C2×#14583811 | C22 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 14. #19149676 | C22 | semidirect |
| 15. #19149667 | C22 | semidirect |
| 18. #19149590 | C22 | semidirect |
| 19. C4×#13063436 | C22 | semidirect |
| 34. #14583810 | D4 | semidirect |
| 57. #13063436 | C2×D4 | semidirect |
| 82. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 90. C173 | #3151 | semidirect |
| 94. C2×#127 | D173 | semidirect |
| 174. 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 |
| #26011878 | 2 |
| #26011867 | 2 |
| #26011863 | 2 |
| C4×#14583810 | 2 |
| C2×#127×C173 | 2 |
| #3151 | 173 |