Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #26011965 | C2 | semidirect |
| 3. #26011604 | C2 | semidirect |
| 4. C4×D1384 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011497 | C2 | semidirect |
| 7. #405×C173 | C2 | semidirect |
| 9. C2×D1384 | C4 | semidirect |
| 12. C4×D692 | C22 | semidirect |
| 16. #19149613 | C22 | semidirect |
| 17. #19149611 | C22 | semidirect |
| 18. #19149601 | C22 | semidirect |
| 22. #97×C173 | C22 | semidirect |
| 23. C4×C8×C173 | C22 | semidirect |
| 27. C2×D692 | C2×C4 | semidirect |
| 30. D1384 | C2×C4 | semidirect |
| 31. D1384 | C2×C4 | semidirect |
| 38. C2×C8×C173 | C2×C4 | semidirect |
| 77. C173 | #2948 | semidirect |
| 85. #405 | D173 | semidirect |
| 100. #97 | C2×D173 | semidirect |
| 101. C4×C8 | C2×D173 | semidirect |
| 112. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1384 | 2 |
| #26011965 | 2 |
| #26011604 | 2 |
| C4×D1384 | 2 |
| #26011529 | 2 |
| #26011497 | 2 |
| #405×C173 | 2 |
| #2948 | 173 |