Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #26012440 | C2 | semidirect |
| 3. #26012436 | C2 | semidirect |
| 4. C4⋊C4×#10621924 | C2 | semidirect |
| 6. C42×#10621924 | C2 | semidirect |
| 18. #19149674 | C4 | semidirect |
| 19. #19149673 | C4 | semidirect |
| 20. #19149672 | C4 | semidirect |
| 24. #126×C173 | C4 | semidirect |
| 38. C4⋊Dic173 | C2×C4 | semidirect |
| 39. #14583805 | C2×C4 | semidirect |
| 40. #14583805 | C2×C4 | semidirect |
| 44. C4×Dic173 | C2×C4 | semidirect |
| 45. C4⋊C4×C173 | C2×C4 | semidirect |
| 47. C42×C173 | C2×C4 | semidirect |
| 80. #10621924 | #126 | direct (N × H) |
| 90. C173 | C4×#126 | semidirect |
| 103. #126 | #10621924 | direct (N × H) |
| 128. C4⋊C4 | C2×#10621924 | semidirect |
| 138. C42 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012441 | 2 |
| #26012440 | 2 |
| #26012436 | 2 |
| C4⋊C4×#10621924 | 2 |
| C22⋊C4×#10621924 | 2 |
| C42×#10621924 | 2 |
| #126×D173 | 2 |
| C4×#126 | 173 |