Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149709 | C2 | semidirect |
| 2. C22×#14583815 | C2 | semidirect |
| 4. #26011968 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011690 | C2 | semidirect |
| 7. #26011517 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. #416×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 23. #19149644 | C22 | semidirect |
| 26. #19149608 | C22 | semidirect |
| 31. #103×C173 | C22 | semidirect |
| 32. #102×C173 | C22 | semidirect |
| 36. C2×Dic346 | D4 | semidirect |
| 116. C173 | #3043 | semidirect |
| 126. #416 | D173 | semidirect |
| 147. #103 | C2×D173 | semidirect |
| 149. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C22×#14583815 | 2 |
| #26012055 | 2 |
| #26011968 | 2 |
| #26011716 | 2 |
| #26011690 | 2 |
| #26011517 | 2 |
| #26011495 | 2 |
| #416×C173 | 2 |
| #3043 | 173 |