Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic346 | C2 | semidirect |
| 4. #26011397 | C2 | semidirect |
| 6. #26011383 | C2 | semidirect |
| 7. #26011365 | C2 | semidirect |
| 8. #26011361 | C2 | semidirect |
| 9. #376×C173 | C2 | semidirect |
| 13. #19149667 | C4 | semidirect |
| 33. C2×Dic346 | C2×C4 | semidirect |
| 48. #14583803 | C2×C4 | semidirect |
| 56. C42×C173 | C2×C4 | semidirect |
| 111. C173 | #2326 | semidirect |
| 121. #376 | D173 | semidirect |
| 168. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| C2×C4×Dic346 | 2 |
| C2×C4×D692 | 2 |
| #26011397 | 2 |
| #26011393 | 2 |
| #26011383 | 2 |
| #26011365 | 2 |
| #26011361 | 2 |
| #376×C173 | 2 |
| #2326 | 173 |