Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 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. #26012395 | C2 | direct (N × H) |
| 6. #19149738 | C22 | semidirect |
| 10. #19149675 | C4 | semidirect |
| 12. C2×C4×Dic173 | C4 | semidirect |
| 13. C22×D4×C173 | C4 | semidirect |
| 28. C4×Dic173 | C2×C4 | semidirect |
| 33. C2×D4×C173 | C2×C4 | semidirect |
| 81. C2×C173 | #353 | semidirect |
| 85. C173 | C2×#353 | semidirect |
| 92. C22×D4 | #10621924 | semidirect |
| 113. C2×D4 | C2×#10621924 | semidirect |
| 169. C2 | #26012395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26012395 | 2 |
| C2×#19149675 | 2 |
| C2×#353 | 173 |