Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19149678 | C2 | semidirect |
| 3. #26011780 | C2 | direct (N × H) |
| 4. C2×#19149610 | C2 | semidirect |
| 5. C2×#19149608 | C2 | semidirect |
| 8. C2×#106×C173 | C2 | semidirect |
| 14. #19149678 | C22 | semidirect |
| 21. #19149610 | C22 | semidirect |
| 22. #19149608 | C22 | semidirect |
| 28. #106×C173 | C22 | semidirect |
| 34. C2×D692 | Q8 | semidirect |
| 65. D692 | C2×Q8 | semidirect |
| 100. C2×C173 | #476 | semidirect |
| 105. C173 | C2×#476 | semidirect |
| 111. C2×#106 | D173 | semidirect |
| 131. #106 | C2×D173 | semidirect |
| 207. C2 | #26011780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149678 | 2 |
| C2×#19149641 | 2 |
| #26011780 | 2 |
| C2×#19149610 | 2 |
| C2×#19149608 | 2 |
| C2×#19149601 | 2 |
| C2×#19149599 | 2 |
| C2×#106×C173 | 2 |
| C2×#476 | 173 |