Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26011968 | C2 | semidirect |
| 4. #26011593 | C2 | semidirect |
| 5. C4×#14583815 | C2 | semidirect |
| 6. #26011529 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 9. #405×C173 | C2 | semidirect |
| 12. C2×#14583815 | C4 | semidirect |
| 15. C4×Dic346 | C22 | semidirect |
| 23. #19149613 | C22 | semidirect |
| 24. #19149611 | C22 | semidirect |
| 25. #19149604 | C22 | semidirect |
| 30. #97×C173 | C22 | semidirect |
| 31. C4×C8×C173 | C22 | semidirect |
| 35. C2×Dic346 | C2×C4 | semidirect |
| 43. #14583815 | C2×C4 | semidirect |
| 44. #14583815 | C2×C4 | semidirect |
| 56. C2×C8×C173 | C2×C4 | semidirect |
| 103. C173 | #2949 | semidirect |
| 113. #405 | D173 | semidirect |
| 134. #97 | C2×D173 | semidirect |
| 135. C4×C8 | C2×D173 | semidirect |
| 151. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| #26011968 | 2 |
| #26011965 | 2 |
| #26011593 | 2 |
| C4×#14583815 | 2 |
| #26011529 | 2 |
| #26011501 | 2 |
| #26011497 | 2 |
| #405×C173 | 2 |
| #2949 | 173 |