Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×M16×D173 | C2 | semidirect |
| 3. C2×#19149606 | C2 | semidirect |
| 4. C4×#14583803 | C2 | semidirect |
| 5. #26011252 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C2×#104×C173 | C2 | semidirect |
| 15. #19149655 | C4 | semidirect |
| 16. #19149655 | C4 | semidirect |
| 17. #19149650 | C4 | semidirect |
| 18. #19149650 | C4 | semidirect |
| 45. #14583810 | D4 | semidirect |
| 73. M16×C173 | D4 | semidirect |
| 139. C2×D173 | #104 | semidirect |
| 159. C173 | #1871 | semidirect |
| 164. C2×#104 | D173 | semidirect |
| 218. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D173 | 2 |
| #26011998 | 2 |
| C2×#19149606 | 2 |
| C4×#14583803 | 2 |
| #26011252 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1871 | 173 |