Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 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×C22⋊#13063436 | C2 | semidirect |
| 2. C4×C22⋊Dic173 | C2 | semidirect |
| 3. #26011228 | C2 | semidirect |
| 4. #26011225 | C2 | semidirect |
| 12. C2×#41×C173 | C4 | semidirect |
| 15. C22⋊Q8×C173 | C4 | semidirect |
| 17. #121×C173 | C4 | semidirect |
| 22. #117×C173 | C4 | semidirect |
| 112. C173 | #1501 | semidirect |
| 119. C2×#41 | Dic173 | semidirect |
| 123. C22⋊Q8 | Dic173 | semidirect |
| 125. #121 | Dic173 | semidirect |
| 130. #117 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13063436 | 2 |
| C4×C22⋊Dic173 | 2 |
| #26011228 | 2 |
| #26011225 | 2 |
| #525×C173 | 2 |
| #1501 | 173 |