Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 162 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. #26012516 | C2 | semidirect |
| 2. #26012515 | C2 | semidirect |
| 3. D173⋊(C4⋊C8) | C2 | semidirect |
| 5. #26012450 | C2 | semidirect |
| 6. C4×D173⋊C8 | C2 | semidirect |
| 10. #19149746 | C22 | semidirect |
| 11. C4⋊#13063443 | C22 | semidirect |
| 14. #19149734 | C22 | semidirect |
| 15. C4×#13063443 | C22 | semidirect |
| 98. D173 | #433 | semidirect |
| 99. C173 | C2×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012516 | 2 |
| #26012515 | 2 |
| D173⋊(C4⋊C8) | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012450 | 2 |
| C4×D173⋊C8 | 2 |
| #117×D173 | 2 |
| C2×#433 | 173 |