Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 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. #26011891 | C2 | semidirect |
| 3. #26011314 | C2 | semidirect |
| 4. #26011313 | C2 | semidirect |
| 5. #26011311 | C2 | semidirect |
| 59. C173 | #2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011891 | 2 |
| #26011608 | 2 |
| #26011314 | 2 |
| #26011313 | 2 |
| #26011311 | 2 |
| #26011301 | 2 |
| #360×C173 | 2 |
| #2231 | 173 |