Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012044 | C2 | semidirect |
| 3. #26011852 | C2 | semidirect |
| 4. #26011847 | C2 | semidirect |
| 5. #26011500 | C2 | semidirect |
| 8. M16×Dic173 | C2 | semidirect |
| 9. #419×C173 | C2 | semidirect |
| 12. #19149678 | C22 | semidirect |
| 13. #19149670 | C22 | semidirect |
| 22. #19149603 | C22 | semidirect |
| 25. #19149589 | C22 | semidirect |
| 26. C8×Dic173 | C22 | semidirect |
| 30. #103×C173 | C22 | semidirect |
| 104. C173 | #3140 | semidirect |
| 111. #419 | D173 | semidirect |
| 131. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×#19149668 | 2 |
| #26011852 | 2 |
| #26011847 | 2 |
| #26011500 | 2 |
| #26011497 | 2 |
| #26011495 | 2 |
| M16×Dic173 | 2 |
| #419×C173 | 2 |
| #3140 | 173 |