Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #26012257 | C2 | semidirect |
| 3. #26011612 | C2 | semidirect |
| 4. #26011607 | C2 | semidirect |
| 5. C2×#19149605 | C2 | semidirect |
| 6. M16×Dic173 | C2 | semidirect |
| 7. #430×C173 | C2 | semidirect |
| 9. #19149712 | C4 | semidirect |
| 10. #19149707 | C4 | semidirect |
| 12. #19149687 | C22 | semidirect |
| 17. #19149605 | C22 | semidirect |
| 18. #19149605 | C22 | semidirect |
| 19. #19149589 | C22 | semidirect |
| 20. C8×Dic173 | C22 | semidirect |
| 23. #108×C173 | C22 | semidirect |
| 33. Dic692 | C2×C4 | semidirect |
| 34. #14583815 | C2×C4 | semidirect |
| 35. D1384 | C2×C4 | semidirect |
| 85. C173 | #2956 | semidirect |
| 91. #430 | D173 | semidirect |
| 105. #108 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| #26012257 | 2 |
| #26011612 | 2 |
| #26011607 | 2 |
| C2×#19149605 | 2 |
| M16×Dic173 | 2 |
| #430×C173 | 2 |
| #2956 | 173 |