Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #26011966 | C2 | semidirect |
| 2. #26011603 | C2 | semidirect |
| 3. D8×Dic173 | C2 | semidirect |
| 4. #26011529 | C2 | semidirect |
| 5. #26011496 | C2 | semidirect |
| 6. #26011446 | C2 | semidirect |
| 10. D4×Dic173 | C22 | semidirect |
| 14. #19149613 | C22 | semidirect |
| 15. #19149611 | C22 | semidirect |
| 16. #19149600 | C22 | semidirect |
| 17. #19149589 | C22 | semidirect |
| 18. C8×Dic173 | C22 | semidirect |
| 20. C2×D8×C173 | C4 | semidirect |
| 37. C2×D4×C173 | C2×C4 | semidirect |
| 40. D8×C173 | C2×C4 | semidirect |
| 41. D8×C173 | C2×C4 | semidirect |
| 42. C2×C8×C173 | C2×C4 | semidirect |
| 77. C173 | #2948 | semidirect |
| 87. C2×D8 | Dic173 | semidirect |
| 105. C2×D4 | C2×Dic173 | semidirect |
| 109. D8 | C2×Dic173 | semidirect |
| 110. D8 | C2×Dic173 | semidirect |
| 113. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011966 | 2 |
| #26011603 | 2 |
| D8×Dic173 | 2 |
| #26011529 | 2 |
| #26011496 | 2 |
| #26011446 | 2 |
| C22×D8×C173 | 2 |
| #2948 | 173 |