Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19149712 | C2 | semidirect |
| 3. C2×#19149667 | C2 | semidirect |
| 4. C4×#14583826 | C2 | semidirect |
| 5. #26011714 | C2 | semidirect |
| 6. #26011707 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011497 | C2 | semidirect |
| 9. #423×C173 | C2 | semidirect |
| 15. C2×Dic692 | C22 | semidirect |
| 17. C2×#14583815 | C22 | semidirect |
| 22. C4×Dic346 | C22 | semidirect |
| 23. C4×D692 | C22 | semidirect |
| 29. #19149604 | C22 | semidirect |
| 34. C4⋊C8×C173 | C22 | semidirect |
| 125. C173 | #3040 | semidirect |
| 133. #423 | D173 | semidirect |
| 158. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149707 | 2 |
| C2×#19149667 | 2 |
| C4×#14583826 | 2 |
| #26011714 | 2 |
| #26011707 | 2 |
| #26011501 | 2 |
| #26011497 | 2 |
| #423×C173 | 2 |
| #3040 | 173 |