Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26011883 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011713 | C2 | semidirect |
| 5. #26011646 | C2 | semidirect |
| 7. #26011548 | C2 | semidirect |
| 8. #533×C173 | C2 | semidirect |
| 11. C2×#14583816 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 20. #19149602 | C22 | semidirect |
| 23. #19149590 | C22 | semidirect |
| 24. C4⋊Q8×C173 | C22 | semidirect |
| 25. C4⋊Q8×C173 | C22 | semidirect |
| 30. C4×Q8×C173 | C22 | semidirect |
| 112. C173 | #3215 | semidirect |
| 114. #533 | D173 | semidirect |
| 126. C4⋊Q8 | C2×D173 | semidirect |
| 127. C4⋊Q8 | C2×D173 | semidirect |
| 136. C4×Q8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| #26011883 | 2 |
| #26011853 | 2 |
| #26011713 | 2 |
| #26011646 | 2 |
| #26011641 | 2 |
| #26011548 | 2 |
| #533×C173 | 2 |
| #3215 | 173 |