Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012025 | C2 | semidirect |
| 2. C2×#19149667 | C2 | semidirect |
| 3. #26011875 | C2 | semidirect |
| 4. #26011846 | C2 | semidirect |
| 5. #26011714 | C2 | semidirect |
| 6. #26011707 | C2 | semidirect |
| 7. #26011649 | C2 | semidirect |
| 8. #26011644 | C2 | semidirect |
| 9. #26011632 | C2 | semidirect |
| 11. #431×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 16. C2×#14583815 | C22 | semidirect |
| 19. #19149671 | C22 | semidirect |
| 24. #19149667 | C22 | semidirect |
| 28. C4×Dic346 | C22 | semidirect |
| 29. C4×D692 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 35. #19149604 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 42. C4×C8×C173 | C22 | semidirect |
| 143. C173 | #3211 | semidirect |
| 155. #431 | D173 | semidirect |
| 179. C4⋊C8 | C2×D173 | semidirect |
| 186. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| C2×#19149667 | 2 |
| #26011875 | 2 |
| #26011846 | 2 |
| #26011714 | 2 |
| #26011707 | 2 |
| #26011649 | 2 |
| #26011644 | 2 |
| #26011632 | 2 |
| #26011627 | 2 |
| #431×C173 | 2 |
| #3211 | 173 |