Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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. #26012439 | C2 | semidirect |
| 2. #26012436 | C2 | semidirect |
| 8. #19149676 | C4 | semidirect |
| 9. #19149675 | C4 | semidirect |
| 11. #127×C173 | C4 | semidirect |
| 16. C2×D692 | C2×C4 | semidirect |
| 17. C2×C22⋊D173 | C2×C4 | semidirect |
| 21. C4×Dic173 | C2×C4 | semidirect |
| 22. C2×D4×C173 | C2×C4 | semidirect |
| 23. C42×C173 | C2×C4 | semidirect |
| 50. C173 | #2380 | semidirect |
| 59. #127 | #10621924 | semidirect |
| 68. C2×D4 | C2×#10621924 | semidirect |
| 74. C42 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012439 | 2 |
| #26012436 | 2 |
| #127×D173 | 2 |
| #2380 | 173 |