Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C2×#19149685 | C2 | semidirect |
| 2. #26012058 | C2 | semidirect |
| 3. #26011741 | C2 | semidirect |
| 4. #26011724 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. C22×D8×C173 | C2 | semidirect |
| 11. C2×#14583809 | C22 | semidirect |
| 12. C2×C8×D173 | C22 | semidirect |
| 15. #19149650 | C22 | semidirect |
| 18. #19149613 | C22 | semidirect |
| 19. #19149611 | C22 | semidirect |
| 20. #19149600 | C22 | semidirect |
| 49. C2×C8×C173 | D4 | semidirect |
| 93. C173 | #3058 | semidirect |
| 95. C22×D8 | D173 | semidirect |
| 139. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149685 | 2 |
| #26012058 | 2 |
| #26011741 | 2 |
| #26011724 | 2 |
| #26011529 | 2 |
| #26011496 | 2 |
| C22×D8×C173 | 2 |
| #3058 | 173 |