Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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×#19149709 | C2 | semidirect |
| 4. C22×#14583816 | C2 | semidirect |
| 5. #26012067 | C2 | semidirect |
| 6. #26011886 | C2 | semidirect |
| 7. #26011883 | C2 | semidirect |
| 8. #26011873 | C2 | semidirect |
| 9. #26011870 | C2 | semidirect |
| 10. #26011447 | C2 | semidirect |
| 11. #536×C173 | C2 | semidirect |
| 143. C173 | #3156 | semidirect |
| 150. #536 | 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×#19149709 | 2 |
| C2×#19149699 | 2 |
| C22×#14583816 | 2 |
| #26012067 | 2 |
| #26011886 | 2 |
| #26011883 | 2 |
| #26011873 | 2 |
| #26011870 | 2 |
| #26011447 | 2 |
| #536×C173 | 2 |
| #3156 | 173 |