Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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. Q8×#13063443 | C2 | semidirect |
| 3. #26012353 | C2 | semidirect |
| 4. Q8⋊#13063443 | C2 | semidirect |
| 6. C8×#13063443 | C2 | semidirect |
| 31. #14583813 | C8 | semidirect |
| 45. #13063443 | SD16 | semidirect |
| 54. #13063436 | C2×C8 | semidirect |
| 56. Q8×C173 | C2×C8 | semidirect |
| 77. C173 | C8×SD16 | semidirect |
| 121. Q8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13063443 | 2 |
| #26012519 | 2 |
| #26012353 | 2 |
| Q8⋊#13063443 | 2 |
| #26012339 | 2 |
| C8×#13063443 | 2 |
| #26011576 | 2 |
| C8×SD16 | 173 |