Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149700 | C2 | semidirect |
| 2. #26012163 | C2 | semidirect |
| 3. #26012161 | C2 | semidirect |
| 4. #26011867 | C2 | semidirect |
| 5. #26011726 | C2 | semidirect |
| 6. #26011692 | C2 | semidirect |
| 7. #26011637 | C2 | semidirect |
| 8. #26011635 | C2 | semidirect |
| 9. C4×#14583816 | C2 | semidirect |
| 10. #26011556 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 58. #14583816 | D4 | semidirect |
| 130. C4×C173 | #135 | semidirect |
| 142. C173 | #3287 | semidirect |
| 150. #460 | D173 | semidirect |
| 276. C4 | #19149700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149700 | 2 |
| #26012163 | 2 |
| #26012161 | 2 |
| #26011867 | 2 |
| #26011726 | 2 |
| #26011692 | 2 |
| #26011637 | 2 |
| #26011635 | 2 |
| C4×#14583816 | 2 |
| #26011556 | 2 |
| #460×C173 | 2 |
| #3287 | 173 |