Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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. #26012050 | C2 | semidirect |
| 2. #26011681 | C2 | semidirect |
| 3. #26011678 | C2 | semidirect |
| 4. C2×#19149594 | C2 | semidirect |
| 5. C2×H(5,𝔽2)×C173 | C2 | semidirect |
| 6. C22×C22⋊D173 | C22 | semidirect |
| 8. #19149660 | C22 | semidirect |
| 11. #19149647 | C22 | semidirect |
| 12. C2×C22⋊Dic173 | C22 | semidirect |
| 13. #19149594 | C22 | semidirect |
| 19. C23×D173 | C23 | semidirect |
| 24. C22×Dic173 | C23 | semidirect |
| 28. C22⋊Dic173 | C23 | semidirect |
| 31. C24×C173 | D4 | semidirect |
| 41. C2×D4×C173 | D4 | semidirect |
| 44. C22×C4×C173 | D4 | semidirect |
| 93. C173 | #3026 | semidirect |
| 95. C2×H(5,𝔽2) | D173 | semidirect |
| 115. C24 | C22⋊D173 | semidirect |
| 128. C2×D4 | C22⋊D173 | semidirect |
| 133. C22×C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012050 | 2 |
| #26011681 | 2 |
| #26011678 | 2 |
| C2×#19149594 | 2 |
| C2×H(5,𝔽2)×C173 | 2 |
| #3026 | 173 |