Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#19149686 | C2 | semidirect |
| 2. #26011613 | C2 | semidirect |
| 3. #26011608 | C2 | semidirect |
| 4. #26011540 | C2 | semidirect |
| 5. #26011508 | C2 | semidirect |
| 6. #26011449 | C2 | semidirect |
| 10. #19149686 | C22 | semidirect |
| 11. #19149686 | C22 | semidirect |
| 17. #19149615 | C22 | semidirect |
| 18. #19149606 | C22 | semidirect |
| 19. #19149589 | C22 | semidirect |
| 20. C8×Dic173 | C22 | semidirect |
| 22. #137×C173 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C173 | C4 | semidirect |
| 89. C173 | #2955 | semidirect |
| 99. #137 | Dic173 | semidirect |
| 100. AGL(1,ℤ/8) | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011613 | 2 |
| #26011608 | 2 |
| #26011540 | 2 |
| #26011508 | 2 |
| #26011449 | 2 |
| #575×C173 | 2 |
| #2955 | 173 |