Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×C4×Dic173 | C2 | semidirect |
| 2. C2×#19149606 | C2 | semidirect |
| 3. #26011455 | C2 | semidirect |
| 4. #26011250 | C2 | semidirect |
| 16. C22⋊Q8×C173 | C4 | semidirect |
| 17. #121×C173 | C4 | semidirect |
| 29. C4×Dic173 | D4 | semidirect |
| 33. C2×Q8×C173 | C2×C4 | semidirect |
| 36. C2×D4×C173 | C2×C4 | semidirect |
| 45. C4⋊C4×C173 | C2×C4 | semidirect |
| 84. C22×C173 | #104 | semidirect |
| 100. C173 | #1896 | semidirect |
| 112. C22⋊Q8 | Dic173 | semidirect |
| 113. #121 | Dic173 | semidirect |
| 125. C2×Q8 | C2×Dic173 | semidirect |
| 128. C2×D4 | C2×Dic173 | semidirect |
| 143. C4⋊C4 | C2×Dic173 | semidirect |
| 185. C22 | #19149606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic173 | 2 |
| C2×#19149606 | 2 |
| #26011455 | 2 |
| #26011250 | 2 |
| #525×C173 | 2 |
| #1896 | 173 |