Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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. #26011998 | C2 | semidirect |
| 2. #26011681 | C2 | semidirect |
| 3. #26011678 | C2 | semidirect |
| 4. #26011465 | C2 | semidirect |
| 5. #585×C173 | C2 | semidirect |
| 6. C22×C4×D173 | C22 | semidirect |
| 7. #19149660 | C22 | semidirect |
| 10. #19149647 | C22 | semidirect |
| 12. #19149638 | C22 | semidirect |
| 13. #19149594 | C22 | semidirect |
| 36. C2×Q8×C173 | D4 | semidirect |
| 39. C2×D4×C173 | D4 | semidirect |
| 42. C22×C4×C173 | D4 | semidirect |
| 82. C173 | #3025 | semidirect |
| 84. #585 | D173 | semidirect |
| 109. C2×Q8 | C22⋊D173 | semidirect |
| 113. C2×D4 | C22⋊D173 | semidirect |
| 119. C22×C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011998 | 2 |
| #26011681 | 2 |
| #26011678 | 2 |
| #26011465 | 2 |
| #585×C173 | 2 |
| #3025 | 173 |