Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 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. #26011931 | C2 | semidirect |
| 2. #26011874 | C2 | semidirect |
| 3. #26011608 | C2 | semidirect |
| 4. #26011311 | C2 | semidirect |
| 5. #26011308 | C2 | semidirect |
| 6. #26011304 | C2 | semidirect |
| 74. C173 | #2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011931 | 2 |
| #26011874 | 2 |
| #26011608 | 2 |
| #26011311 | 2 |
| #26011308 | 2 |
| #26011304 | 2 |
| #509×C173 | 2 |
| #2212 | 173 |