Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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. #26012122 | C2 | direct (N × H) |
| 2. C2×#19149678 | C2 | semidirect |
| 3. C2×#19149670 | C2 | semidirect |
| 8. #19149678 | C22 | semidirect |
| 9. #19149670 | C22 | semidirect |
| 34. C22×C4×C173 | Q8 | semidirect |
| 53. C2×C4×C173 | C2×Q8 | semidirect |
| 69. C2×C173 | #544 | semidirect |
| 73. C173 | C2×#544 | semidirect |
| 102. C22×C4 | Dic346 | semidirect |
| 127. C2×C4 | C2×Dic346 | semidirect |
| 143. C2 | #26012122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012122 | 2 |
| C2×#19149678 | 2 |
| C2×#19149670 | 2 |
| C2×#19149658 | 2 |
| C2×#19149638 | 2 |
| C22×C4⋊C4×C173 | 2 |
| C2×#544 | 173 |