Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26011909 | C2 | semidirect |
| 2. #26011908 | C2 | semidirect |
| 4. #26011311 | C2 | semidirect |
| 5. #26011274 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. #350×C173 | C2 | semidirect |
| 71. C173 | #2170 | semidirect |
| 78. #350 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011909 | 2 |
| #26011908 | 2 |
| #26011606 | 2 |
| #26011311 | 2 |
| #26011274 | 2 |
| C16×Dic173 | 2 |
| #350×C173 | 2 |
| #2170 | 173 |