Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012043 | C2 | semidirect |
| 3. #26011884 | C2 | semidirect |
| 4. #26011852 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011715 | C2 | semidirect |
| 7. #26011647 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #451×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 16. #19149678 | C22 | semidirect |
| 17. #19149677 | C22 | semidirect |
| 25. Q8×Dic173 | C22 | semidirect |
| 27. #19149644 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 39. C2×Q16×C173 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 139. C173 | #3215 | semidirect |
| 148. #451 | D173 | semidirect |
| 155. C2×Q16 | C2×D173 | semidirect |
| 177. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| C2×#19149668 | 2 |
| #26011884 | 2 |
| #26011852 | 2 |
| #26011716 | 2 |
| #26011715 | 2 |
| #26011647 | 2 |
| #26011644 | 2 |
| #26011641 | 2 |
| #26011545 | 2 |
| #451×C173 | 2 |
| #3215 | 173 |