Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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. #26011365 | C2 | semidirect |
| 4. #26011362 | C2 | semidirect |
| 5. #26011351 | C2 | semidirect |
| 6. #26011349 | C2 | semidirect |
| 7. #380×C173 | C2 | semidirect |
| 11. C2×C4⋊Dic173 | C22 | semidirect |
| 12. C2×#14583805 | C22 | semidirect |
| 14. C2×#14583803 | C4 | semidirect |
| 19. #19149586 | C22 | semidirect |
| 20. #19149586 | C22 | semidirect |
| 22. C2×C4⋊C4×C173 | C22 | semidirect |
| 24. #95×C173 | C22 | semidirect |
| 32. C22×Dic173 | C2×C4 | semidirect |
| 42. #14583803 | C2×C4 | semidirect |
| 43. #14583803 | C2×C4 | semidirect |
| 46. C22×C4×C173 | C2×C4 | semidirect |
| 58. C22×D173 | C4⋊C4 | semidirect |
| 111. C173 | #2315 | semidirect |
| 119. #380 | D173 | semidirect |
| 126. C2×C4⋊C4 | C2×D173 | semidirect |
| 136. #95 | C2×D173 | semidirect |
| 152. C22×C4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583803 | 2 |
| C2×C22⋊C4×D173 | 2 |
| #26011365 | 2 |
| #26011362 | 2 |
| #26011351 | 2 |
| #26011349 | 2 |
| #380×C173 | 2 |
| #2315 | 173 |