Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #26011364 | C2 | semidirect |
| 4. #26011363 | C2 | semidirect |
| 5. #26011349 | C2 | semidirect |
| 9. C2×#14583805 | C22 | semidirect |
| 11. C2×C22⋊Dic173 | C4 | semidirect |
| 16. #19149586 | C22 | semidirect |
| 25. C22×Dic173 | C2×C4 | semidirect |
| 31. C22⋊Dic173 | C2×C4 | semidirect |
| 32. C22⋊Dic173 | C2×C4 | semidirect |
| 57. C23×C173 | C4⋊C4 | semidirect |
| 98. C173 | #2315 | semidirect |
| 150. C23 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic173 | 2 |
| #26011364 | 2 |
| #26011363 | 2 |
| #26011349 | 2 |
| C22×C22⋊C4×C173 | 2 |
| #2315 | 173 |