Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#14583813 | C2 | semidirect |
| 3. #26011965 | C2 | semidirect |
| 4. #26011703 | C2 | semidirect |
| 5. #26011693 | C2 | semidirect |
| 6. #26011518 | C2 | semidirect |
| 7. #26011500 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. #536×C173 | C2 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 24. #19149603 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 28. C4⋊Q8×C173 | C22 | semidirect |
| 29. #124×C173 | C22 | semidirect |
| 116. C173 | #3042 | semidirect |
| 120. #536 | D173 | semidirect |
| 137. C4⋊Q8 | C2×D173 | semidirect |
| 138. #124 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C22×#14583813 | 2 |
| #26011965 | 2 |
| #26011703 | 2 |
| #26011693 | 2 |
| #26011518 | 2 |
| #26011500 | 2 |
| #26011487 | 2 |
| #536×C173 | 2 |
| #3042 | 173 |