Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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. C173⋊#564 | C2 | semidirect |
| 4. #26011232 | C2 | semidirect |
| 5. #330×C173 | C2 | semidirect |
| 53. C173 | #1658 | semidirect |
| 59. #330 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C173⋊#564 | 2 |
| #26011857 | 2 |
| #26011856 | 2 |
| #26011232 | 2 |
| #330×C173 | 2 |
| #1658 | 173 |