Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D173 | C2 | semidirect |
| 3. C4⋊Q8×D173 | C2 | semidirect |
| 5. #26011886 | C2 | semidirect |
| 6. #26011885 | C2 | semidirect |
| 7. #26011884 | C2 | semidirect |
| 8. #26011883 | C2 | semidirect |
| 9. #26011882 | C2 | semidirect |
| 10. #97×D173 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 15. C2×Dic692 | C22 | semidirect |
| 16. C2×#14583816 | C22 | semidirect |
| 17. C2×#14583816 | C22 | semidirect |
| 24. #19149679 | C22 | semidirect |
| 26. #19149677 | C22 | semidirect |
| 34. #19149590 | C22 | semidirect |
| 35. #19149589 | C22 | semidirect |
| 36. C2×Q16×C173 | C22 | semidirect |
| 38. C4⋊Q8×C173 | C22 | semidirect |
| 40. #97×C173 | C22 | semidirect |
| 130. D173 | #497 | direct (N × H) |
| 131. C173 | C2×#497 | semidirect |
| 142. #497 | D173 | direct (N × H) |
| 151. C2×Q16 | C2×D173 | semidirect |
| 161. C4⋊Q8 | C2×D173 | semidirect |
| 172. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D173 | 2 |
| C2×SD16×D173 | 2 |
| C4⋊Q8×D173 | 2 |
| #124×D173 | 2 |
| #26011886 | 2 |
| #26011885 | 2 |
| #26011884 | 2 |
| #26011883 | 2 |
| #26011882 | 2 |
| #97×D173 | 2 |
| #497×C173 | 2 |
| C2×#497 | 173 |