Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14583811 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 3. #26012060 | C2 | semidirect |
| 4. #26012058 | C2 | semidirect |
| 5. #26011743 | C2 | semidirect |
| 6. #26011726 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011497 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 16. C2×#14583809 | C22 | semidirect |
| 18. C2×C8×D173 | C22 | semidirect |
| 23. #19149654 | C22 | semidirect |
| 24. #19149650 | C22 | semidirect |
| 28. #19149612 | C22 | semidirect |
| 29. #19149610 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 34. #102×C173 | C22 | semidirect |
| 51. C2×#13063436 | D4 | semidirect |
| 125. C173 | #3058 | semidirect |
| 135. #418 | D173 | semidirect |
| 160. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149687 | 2 |
| #26012060 | 2 |
| #26012058 | 2 |
| #26011743 | 2 |
| #26011726 | 2 |
| #26011527 | 2 |
| #26011497 | 2 |
| #418×C173 | 2 |
| #3058 | 173 |