Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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. C22×D173⋊C8 | C2 | semidirect |
| 2. C2×#19149741 | C2 | semidirect |
| 3. #26012433 | C2 | semidirect |
| 4. #26012364 | C2 | semidirect |
| 17. #19149654 | C4 | semidirect |
| 18. #19149653 | C4 | semidirect |
| 21. #19149650 | C4 | semidirect |
| 24. #121×C173 | C4 | semidirect |
| 28. D173⋊C8 | D4 | semidirect |
| 110. C22×C173 | #102 | semidirect |
| 121. C2×D173 | #102 | semidirect |
| 143. C173 | #1893 | semidirect |
| 162. #121 | #10621924 | semidirect |
| 268. C22 | #19149741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| C2×#19149741 | 2 |
| #26012433 | 2 |
| #26012364 | 2 |
| #121×D173 | 2 |
| #1893 | 173 |