Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #26011532 | C2 | semidirect |
| 4. #26011530 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011527 | C2 | semidirect |
| 7. #427×C173 | C2 | semidirect |
| 9. C2×#14583809 | C4 | semidirect |
| 20. #19149613 | C22 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149611 | C22 | semidirect |
| 23. #19149610 | C22 | semidirect |
| 26. #107×C173 | C22 | semidirect |
| 27. #106×C173 | C22 | semidirect |
| 35. #14583809 | C2×C4 | semidirect |
| 36. #14583809 | C2×C4 | semidirect |
| 37. C2×#13063436 | C2×C4 | semidirect |
| 46. C2×C8×C173 | C2×C4 | semidirect |
| 87. C173 | #2911 | semidirect |
| 95. #427 | D173 | semidirect |
| 112. #107 | C2×D173 | semidirect |
| 115. #106 | C2×D173 | semidirect |
| 128. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| #117×D173 | 2 |
| #26011532 | 2 |
| #26011530 | 2 |
| #26011529 | 2 |
| #26011527 | 2 |
| #427×C173 | 2 |
| #2911 | 173 |