Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26012039 | C2 | semidirect |
| 2. C4×D4×D173 | C2 | semidirect |
| 3. #26011803 | C2 | semidirect |
| 4. #26011772 | C2 | semidirect |
| 5. #26011771 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011623 | C2 | semidirect |
| 8. D8×Dic173 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. #26011543 | C2 | semidirect |
| 11. #459×C173 | C2 | semidirect |
| 16. #19149679 | C22 | semidirect |
| 23. D4×Dic173 | C22 | semidirect |
| 30. #19149613 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. C4⋊#13063436 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 39. #127×C173 | C22 | semidirect |
| 41. C4⋊C8×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 91. D692 | #41 | semidirect |
| 107. C4×D173 | D8 | semidirect |
| 116. D4×C173 | #41 | semidirect |
| 154. C173 | #3100 | semidirect |
| 162. #459 | D173 | semidirect |
| 173. #127 | C2×D173 | semidirect |
| 191. C4⋊C8 | C2×D173 | semidirect |
| 195. #102 | C2×D173 | semidirect |
| 256. D4 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| C4×D4×D173 | 2 |
| #26011803 | 2 |
| #26011772 | 2 |
| #26011771 | 2 |
| #26011683 | 2 |
| #26011623 | 2 |
| D8×Dic173 | 2 |
| #26011571 | 2 |
| #26011543 | 2 |
| #459×C173 | 2 |
| #3100 | 173 |