Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#14583825 | C2 | semidirect |
| 2. C2×#19149709 | C2 | semidirect |
| 3. #26011998 | C2 | semidirect |
| 4. #26011650 | C2 | semidirect |
| 5. #26011633 | C2 | semidirect |
| 6. #26011501 | C2 | semidirect |
| 7. #26011496 | C2 | semidirect |
| 8. #26011454 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 19. C2×#14583816 | C22 | semidirect |
| 20. C2×#14583814 | C22 | semidirect |
| 23. #19149655 | C22 | semidirect |
| 24. #19149650 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 29. #19149600 | C22 | semidirect |
| 30. #19149591 | C22 | semidirect |
| 34. C2×SD16×C173 | C22 | semidirect |
| 35. C2×D8×C173 | C22 | semidirect |
| 43. C2×Dic346 | D4 | semidirect |
| 73. C2×D4×C173 | D4 | semidirect |
| 145. C173 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 170. C2×SD16 | C2×D173 | semidirect |
| 171. C2×D8 | C2×D173 | semidirect |
| 201. C2×D4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583825 | 2 |
| C2×#19149709 | 2 |
| #26011998 | 2 |
| #26011650 | 2 |
| #26011633 | 2 |
| #26011501 | 2 |
| #26011496 | 2 |
| #26011454 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3005 | 173 |