Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19149593 | C2 | semidirect |
| 3. #26011347 | C2 | semidirect |
| 4. #26011257 | C2 | semidirect |
| 5. C22×C22⋊C4×C173 | C2 | semidirect |
| 6. C22×C22⋊D173 | C4 | semidirect |
| 12. C2×C22⋊Dic173 | C4 | semidirect |
| 21. C23×D173 | C2×C4 | semidirect |
| 30. C22×Dic173 | C2×C4 | semidirect |
| 31. C22×Dic173 | C2×C4 | semidirect |
| 52. C22⋊C4×C173 | D4 | semidirect |
| 108. C22×C173 | #99 | semidirect |
| 130. C173 | #1898 | semidirect |
| 133. C22×C22⋊C4 | D173 | semidirect |
| 183. C22⋊C4 | C22⋊D173 | semidirect |
| 242. C22 | #19149593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149648 | 2 |
| C2×#19149593 | 2 |
| #26011347 | 2 |
| #26011257 | 2 |
| C22×C22⋊C4×C173 | 2 |
| #1898 | 173 |