Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#19149726 | C2 | semidirect |
| 2. C22×#14583814 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011633 | C2 | semidirect |
| 5. #26011628 | C2 | semidirect |
| 6. #26011501 | C2 | semidirect |
| 7. #26011487 | C2 | semidirect |
| 8. #26011459 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 15. C2×#14583825 | C22 | semidirect |
| 18. C2×Q8×D173 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149603 | C22 | semidirect |
| 29. #19149600 | C22 | semidirect |
| 30. #19149591 | C22 | semidirect |
| 48. C2×Dic346 | D4 | semidirect |
| 69. #41×C173 | D4 | semidirect |
| 145. C173 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 191. #41 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| C22×#14583814 | 2 |
| #26012058 | 2 |
| #26011633 | 2 |
| #26011628 | 2 |
| #26011501 | 2 |
| #26011487 | 2 |
| #26011459 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3010 | 173 |