Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 11. #97×C173 | C4 | semidirect |
| 12. C4×C8×C173 | C4 | semidirect |
| 52. C173 | #1841 | semidirect |
| 64. #97 | Dic173 | semidirect |
| 65. C4×C8 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011262 | 2 |
| #26011251 | 2 |
| #26011249 | 2 |
| #26011248 | 2 |
| C4×M16×C173 | 2 |
| #1841 | 173 |