Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26011540 | C2 | semidirect |
| 5. C4×#14583810 | C2 | semidirect |
| 6. #26011261 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 16. #19149597 | C4 | semidirect |
| 17. #19149595 | C4 | semidirect |
| 95. C173 | #1932 | semidirect |
| 103. #339 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011540 | 2 |
| #26011509 | 2 |
| C2×#19149607 | 2 |
| #26011473 | 2 |
| C4×#14583810 | 2 |
| #26011261 | 2 |
| #339×C173 | 2 |
| #1932 | 173 |