Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 8. #19149615 | C4 | semidirect |
| 9. #19149613 | C4 | semidirect |
| 10. #19149611 | C4 | semidirect |
| 16. #97×C173 | C4 | semidirect |
| 62. C173 | #1773 | semidirect |
| 78. #97 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149615 | 2 |
| #26011529 | 2 |
| #26011446 | 2 |
| #26011251 | 2 |
| C2×#97×C173 | 2 |
| #1773 | 173 |