Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#19149738 | C2 | semidirect |
| 2. #26012397 | C2 | semidirect |
| 3. #26012395 | C2 | semidirect |
| 9. #19149675 | C4 | semidirect |
| 11. #19149668 | C4 | semidirect |
| 15. #19149638 | C4 | semidirect |
| 16. C2×#41×C173 | C4 | semidirect |
| 31. C4×Dic173 | C2×C4 | semidirect |
| 32. C4×Dic173 | C2×C4 | semidirect |
| 34. C2×Q8×C173 | C2×C4 | semidirect |
| 36. C2×D4×C173 | C2×C4 | semidirect |
| 86. C173 | #2127 | semidirect |
| 92. C2×#41 | #10621924 | semidirect |
| 106. C2×Q8 | C2×#10621924 | semidirect |
| 114. C2×D4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26012397 | 2 |
| #26012395 | 2 |
| #26012055 | 2 |
| #2127 | 173 |