Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26011386 | C2 | semidirect |
| 4. #26011372 | C2 | semidirect |
| 6. #26011359 | C2 | semidirect |
| 7. #384×C173 | C2 | semidirect |
| 9. #19149673 | C4 | semidirect |
| 28. #14583805 | C2×C4 | semidirect |
| 37. C42×C173 | C2×C4 | semidirect |
| 72. C173 | #2383 | semidirect |
| 79. #384 | D173 | semidirect |
| 110. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149673 | 2 |
| #26011386 | 2 |
| #26011381 | 2 |
| #26011372 | 2 |
| #26011362 | 2 |
| #26011359 | 2 |
| #384×C173 | 2 |
| #2383 | 173 |