Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 2. #26012427 | C2 | direct (N × H) |
| 6. C2×C4×#10621924 | C4 | semidirect |
| 11. C2×C4×Dic173 | C4 | semidirect |
| 12. C2×C4×Dic173 | C4 | semidirect |
| 13. C42×D173 | C4 | semidirect |
| 15. C2×C42×C173 | C4 | semidirect |
| 19. C4×#10621924 | C2×C4 | semidirect |
| 29. C4×Dic173 | C2×C4 | semidirect |
| 30. C4×Dic173 | C2×C4 | semidirect |
| 33. C42×C173 | C2×C4 | semidirect |
| 67. C2×C173 | #376 | semidirect |
| 70. D173 | #376 | semidirect |
| 72. C173 | C2×#376 | semidirect |
| 87. C2×C42 | #10621924 | semidirect |
| 106. C42 | C2×#10621924 | semidirect |
| 142. C2 | #26012427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10621924 | 2 |
| #26012427 | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| C2×C42×D173 | 2 |
| C2×#376 | 173 |