Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 9. #19149750 | C4 | semidirect |
| 10. #19149749 | C4 | semidirect |
| 17. #19149615 | C4 | semidirect |
| 18. #19149614 | C4 | semidirect |
| 19. #108×C173 | C4 | semidirect |
| 70. C173 | #1778 | semidirect |
| 86. #108 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#108 | 2 |
| M16×#10621924 | 2 |
| C2×#19149733 | 2 |
| #26012366 | 2 |
| #108×D173 | 2 |
| #1778 | 173 |