Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149709 | C2 | semidirect |
| 3. C2×#19149667 | C2 | semidirect |
| 4. #26011713 | C2 | semidirect |
| 5. #26011706 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 7. #26011499 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. C4×#41×C173 | C2 | semidirect |
| 14. C2×#14583816 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 24. C4⋊#13063436 | C22 | semidirect |
| 25. #19149602 | C22 | semidirect |
| 28. C4×Q8×C173 | C22 | semidirect |
| 30. C4×D4×C173 | C22 | semidirect |
| 125. C173 | #3040 | semidirect |
| 130. C4×#41 | D173 | semidirect |
| 150. C4×Q8 | C2×D173 | semidirect |
| 152. C4×D4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149704 | 2 |
| C2×#19149667 | 2 |
| #26011713 | 2 |
| #26011706 | 2 |
| #26011515 | 2 |
| #26011499 | 2 |
| #26011495 | 2 |
| C4×#41×C173 | 2 |
| #3040 | 173 |