Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C2×#19149742 | C2 | semidirect |
| 4. #26012364 | C2 | semidirect |
| 16. #19149659 | C4 | semidirect |
| 17. #19149658 | C4 | semidirect |
| 20. #19149655 | C4 | semidirect |
| 24. C22⋊Q8×C173 | C4 | semidirect |
| 97. C22×C173 | #103 | semidirect |
| 103. C2×D173 | #103 | semidirect |
| 125. C173 | #1892 | semidirect |
| 143. C22⋊Q8 | #10621924 | semidirect |
| 232. C22 | #19149742 | 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×#19149742 | 2 |
| #26012433 | 2 |
| #26012364 | 2 |
| C22⋊Q8×D173 | 2 |
| #1892 | 173 |