Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19149699 | C2 | semidirect |
| 2. C22×C8×D173 | C2 | semidirect |
| 3. #26012003 | C2 | semidirect |
| 4. #26011998 | C2 | semidirect |
| 5. #26011731 | C2 | semidirect |
| 6. #26011726 | C2 | semidirect |
| 7. #26011723 | C2 | semidirect |
| 8. #26011719 | C2 | semidirect |
| 9. #26011527 | C2 | semidirect |
| 10. #26011488 | C2 | semidirect |
| 11. #416×C173 | C2 | semidirect |
| 15. C2×#14583816 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 17. C2×#14583813 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 34. #19149612 | C22 | semidirect |
| 35. #19149610 | C22 | semidirect |
| 36. #19149604 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 61. C2×#13063436 | D4 | semidirect |
| 133. C2×D173 | #135 | semidirect |
| 148. C173 | #3050 | semidirect |
| 160. #416 | D173 | semidirect |
| 189. #103 | C2×D173 | semidirect |
| 191. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| C22×C8×D173 | 2 |
| #26012003 | 2 |
| #26011998 | 2 |
| #26011731 | 2 |
| #26011726 | 2 |
| #26011723 | 2 |
| #26011719 | 2 |
| #26011527 | 2 |
| #26011488 | 2 |
| #416×C173 | 2 |
| #3050 | 173 |