Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #26011545 | C2 | semidirect |
| 3. #26011541 | C2 | semidirect |
| 4. #26011514 | C2 | semidirect |
| 6. M16×Dic173 | C2 | semidirect |
| 17. #19149608 | C22 | semidirect |
| 19. #19149589 | C22 | semidirect |
| 20. C8×Dic173 | C22 | semidirect |
| 56. C2×Dic173 | M16 | semidirect |
| 92. C173 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic173 | 2 |
| #26011545 | 2 |
| #26011541 | 2 |
| #26011514 | 2 |
| #26011455 | 2 |
| M16×Dic173 | 2 |
| #407×C173 | 2 |
| #2920 | 173 |