Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19149702 | C2 | semidirect |
| 2. #26012160 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011727 | C2 | semidirect |
| 5. #26011724 | C2 | semidirect |
| 6. #26011689 | C2 | semidirect |
| 7. #26011636 | C2 | semidirect |
| 8. #26011635 | C2 | semidirect |
| 9. Q16×Dic173 | C2 | semidirect |
| 10. C8×C22⋊D173 | C2 | semidirect |
| 11. C2×#135×C173 | C2 | semidirect |
| 74. Q16×C173 | D4 | semidirect |
| 134. Dic173 | #135 | semidirect |
| 142. C173 | #3287 | semidirect |
| 145. C2×#135 | D173 | semidirect |
| 202. Q16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| #26012160 | 2 |
| #26011866 | 2 |
| #26011727 | 2 |
| #26011724 | 2 |
| #26011689 | 2 |
| #26011636 | 2 |
| #26011635 | 2 |
| Q16×Dic173 | 2 |
| C8×C22⋊D173 | 2 |
| C2×#135×C173 | 2 |
| #3287 | 173 |