Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19149685 | C2 | semidirect |
| 3. #26011614 | C2 | direct (N × H) |
| 4. C2×#19149615 | C2 | semidirect |
| 5. C2×#19149607 | C2 | semidirect |
| 6. C2×#97×C173 | C2 | semidirect |
| 8. #19149701 | C4 | semidirect |
| 10. C2×Dic692 | C4 | semidirect |
| 11. C2×#14583815 | C4 | semidirect |
| 12. C2×D1384 | C4 | semidirect |
| 14. #19149685 | C22 | semidirect |
| 18. #19149615 | C22 | semidirect |
| 19. #19149607 | C22 | semidirect |
| 23. #97×C173 | C22 | semidirect |
| 32. Dic692 | C2×C4 | semidirect |
| 33. #14583815 | C2×C4 | semidirect |
| 34. D1384 | C2×C4 | semidirect |
| 88. C2×C173 | #444 | semidirect |
| 91. C173 | C2×#444 | semidirect |
| 98. C2×#97 | D173 | semidirect |
| 115. #97 | C2×D173 | semidirect |
| 181. C2 | #26011614 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149685 | 2 |
| #26011614 | 2 |
| C2×#19149615 | 2 |
| C2×#19149607 | 2 |
| C2×#97×C173 | 2 |
| C2×#444 | 173 |