Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19149671 | C2 | semidirect |
| 3. #26011860 | C2 | semidirect |
| 4. #26011856 | C2 | semidirect |
| 5. #26011846 | C2 | semidirect |
| 6. #26011493 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 77. C173 | #3142 | semidirect |
| 85. C4×M16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149671 | 2 |
| #26011860 | 2 |
| #26011856 | 2 |
| #26011846 | 2 |
| #26011493 | 2 |
| C4×M16×C173 | 2 |
| #3142 | 173 |