Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #26011974 | C2 | semidirect |
| 3. #26011497 | C2 | semidirect |
| 4. #26011493 | C2 | semidirect |
| 5. #26011488 | C2 | semidirect |
| 6. C2×#19149601 | C2 | semidirect |
| 7. C2×#131×C173 | C2 | semidirect |
| 9. #19149725 | C4 | semidirect |
| 16. #19149638 | C22 | semidirect |
| 17. C2×C4⋊Dic173 | C22 | semidirect |
| 18. #19149604 | C22 | semidirect |
| 19. #19149604 | C22 | semidirect |
| 20. #19149601 | C22 | semidirect |
| 21. #19149601 | C22 | semidirect |
| 22. #19149601 | C22 | semidirect |
| 25. C2×M16×C173 | C22 | semidirect |
| 26. C22×C8×C173 | C22 | semidirect |
| 30. #14583826 | C2×C4 | semidirect |
| 34. C2×D692 | C2×C4 | semidirect |
| 97. C173 | #2897 | semidirect |
| 100. C2×#131 | D173 | semidirect |
| 114. C2×M16 | C2×D173 | semidirect |
| 115. C22×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| #26011974 | 2 |
| #26011497 | 2 |
| #26011493 | 2 |
| #26011488 | 2 |
| C2×#19149601 | 2 |
| C2×#131×C173 | 2 |
| #2897 | 173 |