Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012201 | C2 | semidirect |
| 3. #26011838 | C2 | semidirect |
| 4. #26011811 | C2 | semidirect |
| 5. #26011781 | C2 | semidirect |
| 6. #26011723 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011640 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #102×D173 | C2 | semidirect |
| 11. C4×SD16×C173 | C2 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 15. C2×C8×D173 | C22 | semidirect |
| 16. #19149679 | C22 | semidirect |
| 20. #19149655 | C22 | semidirect |
| 26. C4⋊C4×D173 | C22 | semidirect |
| 27. #19149610 | C22 | semidirect |
| 28. C4⋊#13063436 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 32. #19149599 | C22 | semidirect |
| 33. #19149591 | C22 | semidirect |
| 35. C4×Q8×C173 | C22 | semidirect |
| 37. #106×C173 | C22 | semidirect |
| 38. #103×C173 | C22 | semidirect |
| 40. C4×C8×C173 | C22 | semidirect |
| 88. D692 | SD16 | semidirect |
| 136. C173 | #3295 | semidirect |
| 146. C4×SD16 | D173 | semidirect |
| 162. C4×Q8 | C2×D173 | semidirect |
| 168. #106 | C2×D173 | semidirect |
| 170. #103 | C2×D173 | semidirect |
| 177. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| D4×D692 | 2 |
| #26011838 | 2 |
| #26011811 | 2 |
| #26011781 | 2 |
| #26011723 | 2 |
| #26011691 | 2 |
| #26011640 | 2 |
| C8×D692 | 2 |
| #102×D173 | 2 |
| C4×SD16×C173 | 2 |
| #3295 | 173 |