Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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. C2×C4×C22⋊D173 | C2 | semidirect |
| 3. #26011370 | C2 | semidirect |
| 4. #26011364 | C2 | semidirect |
| 5. #26011347 | C2 | semidirect |
| 6. C4×C22⋊Dic173 | C2 | semidirect |
| 7. C24×C4×C173 | C2 | semidirect |
| 9. C22×C4×D173 | C22 | semidirect |
| 10. #19149648 | C4 | direct (N × H) |
| 12. C2×#14583805 | C22 | semidirect |
| 16. C2×#14583803 | C22 | semidirect |
| 17. C2×C4×Dic173 | C22 | semidirect |
| 18. #19149586 | C22 | semidirect |
| 26. C2×C22⋊D173 | C2×C4 | semidirect |
| 34. C22⋊Dic173 | C2×C4 | semidirect |
| 39. C24×C173 | C2×C4 | semidirect |
| 45. C22×C4×C173 | D4 | semidirect |
| 50. C22×D173 | C22×C4 | semidirect |
| 57. C2×Dic173 | C22×C4 | semidirect |
| 78. C22×C173 | C4×D4 | semidirect |
| 86. C4×C173 | #120 | semidirect |
| 95. C173 | C4×#120 | semidirect |
| 97. C24×C4 | D173 | semidirect |
| 122. C24 | C4×D173 | semidirect |
| 135. C22×C4 | C22⋊D173 | semidirect |
| 177. C22 | C4×C22⋊D173 | semidirect |
| 185. C4 | #19149648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149648 | 2 |
| C2×C4×C22⋊D173 | 2 |
| #26011370 | 2 |
| #26011364 | 2 |
| #26011347 | 2 |
| C4×C22⋊Dic173 | 2 |
| C24×C4×C173 | 2 |
| C4×#120 | 173 |