Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26011966 | C2 | semidirect |
| 3. #26011965 | C2 | semidirect |
| 4. #26011600 | C2 | semidirect |
| 5. #26011571 | C2 | semidirect |
| 6. #26011527 | C2 | semidirect |
| 7. #26011497 | C2 | semidirect |
| 8. #26011449 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 11. C2×#14583811 | C4 | semidirect |
| 17. D4×Dic173 | C22 | semidirect |
| 18. #19149641 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149601 | C22 | semidirect |
| 26. #19149589 | C22 | semidirect |
| 27. C8×Dic173 | C22 | semidirect |
| 31. #102×C173 | C22 | semidirect |
| 35. C2×D692 | C2×C4 | semidirect |
| 39. #14583811 | C2×C4 | semidirect |
| 40. #14583811 | C2×C4 | semidirect |
| 41. C2×#13063436 | C2×C4 | semidirect |
| 55. C2×D4×C173 | C2×C4 | semidirect |
| 108. C173 | #2948 | semidirect |
| 117. #418 | D173 | semidirect |
| 138. #102 | C2×D173 | semidirect |
| 149. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| #26011966 | 2 |
| #26011965 | 2 |
| #26011600 | 2 |
| #26011571 | 2 |
| #26011527 | 2 |
| #26011497 | 2 |
| #26011449 | 2 |
| #418×C173 | 2 |
| #2948 | 173 |