Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19149593 | C2 | semidirect |
| 3. #26011371 | C2 | semidirect |
| 4. #26011368 | C2 | semidirect |
| 5. C2×#99×C173 | C2 | semidirect |
| 8. #19149724 | C4 | semidirect |
| 14. C23×Dic173 | C22 | semidirect |
| 16. C2×C22⋊Dic173 | C22 | semidirect |
| 22. C2×C22⋊C4×C173 | C22 | semidirect |
| 70. C22×D173 | C22⋊C4 | semidirect |
| 89. C2×Dic173 | C22⋊C4 | semidirect |
| 97. C23×C173 | C22⋊C4 | semidirect |
| 110. C2×C4×C173 | C22⋊C4 | semidirect |
| 148. C173 | #1790 | semidirect |
| 152. C2×#99 | D173 | semidirect |
| 168. C2×C22⋊C4 | C2×D173 | semidirect |
| 226. C23 | #14583803 | semidirect |
| 259. C2×C4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149593 | 2 |
| #26011371 | 2 |
| #26011368 | 2 |
| C2×#99×C173 | 2 |
| #1790 | 173 |