Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 2. #26011788 | C2 | semidirect |
| 3. #26011778 | C2 | semidirect |
| 4. #26011768 | C2 | semidirect |
| 5. #26011534 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 8. #533×C173 | C2 | semidirect |
| 18. #19149612 | C22 | semidirect |
| 19. #19149610 | C22 | semidirect |
| 20. C4⋊#13063436 | C22 | semidirect |
| 21. C4⋊#13063436 | C22 | semidirect |
| 24. C4⋊Q8×C173 | C22 | semidirect |
| 25. C4⋊Q8×C173 | C22 | semidirect |
| 26. #125×C173 | C22 | semidirect |
| 36. C2×D692 | Q8 | semidirect |
| 115. C173 | #3077 | semidirect |
| 117. #533 | D173 | semidirect |
| 128. C4⋊Q8 | C2×D173 | semidirect |
| 129. C4⋊Q8 | C2×D173 | semidirect |
| 130. #125 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011788 | 2 |
| #26011778 | 2 |
| #26011768 | 2 |
| #26011534 | 2 |
| #26011515 | 2 |
| #26011495 | 2 |
| #533×C173 | 2 |
| #3077 | 173 |