Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
142 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 2. #26011528 | C2 | semidirect |
| 3. #26011318 | C2 | semidirect |
| 4. #26011317 | C2 | semidirect |
| 5. #26011292 | C2 | semidirect |
| 6. #26011270 | C2 | semidirect |
| 7. #357×C173 | C2 | semidirect |
| 69. C173 | #2234 | semidirect |
| 76. #357 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011724 | 2 |
| #26011528 | 2 |
| #26011318 | 2 |
| #26011317 | 2 |
| #26011292 | 2 |
| #26011270 | 2 |
| #357×C173 | 2 |
| #2234 | 173 |