Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1224 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 289 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. C24×Dic173 | C2 | semidirect |
| 2. C2×D4×Dic173 | C2 | semidirect |
| 3. #26011371 | C2 | semidirect |
| 4. #26011366 | C2 | semidirect |
| 5. #26011347 | C2 | semidirect |
| 6. C22⋊C4×Dic173 | C2 | semidirect |
| 11. C23×Dic173 | C22 | semidirect |
| 13. C2×C4⋊Dic173 | C22 | semidirect |
| 16. C2×C22⋊Dic173 | C22 | semidirect |
| 17. C2×C4×Dic173 | C22 | semidirect |
| 18. #19149586 | C22 | semidirect |
| 21. #120×C173 | C4 | semidirect |
| 28. C22×Dic173 | D4 | semidirect |
| 40. C24×C173 | C2×C4 | semidirect |
| 45. C2×D4×C173 | C2×C4 | semidirect |
| 47. C22⋊C4×C173 | C2×C4 | semidirect |
| 65. C23×C173 | C22×C4 | semidirect |
| 72. C2×C4×C173 | C22×C4 | semidirect |
| 81. C22×C173 | C4×D4 | semidirect |
| 89. Dic173 | #120 | direct (N × H) |
| 95. C173 | C4×#120 | semidirect |
| 110. #120 | Dic173 | direct (N × H) |
| 121. C24 | C2×Dic173 | semidirect |
| 126. C2×D4 | C2×Dic173 | semidirect |
| 142. C22⋊C4 | C2×Dic173 | semidirect |
| 152. C23 | C22×Dic173 | semidirect |
| 168. C2×C4 | C22×Dic173 | semidirect |
| 177. C22 | D4×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic173 | 2 |
| C2×D4×Dic173 | 2 |
| #26011371 | 2 |
| #26011366 | 2 |
| #26011347 | 2 |
| C22⋊C4×Dic173 | 2 |
| C2×#120×C173 | 2 |
| C4×#120 | 173 |