Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. D173⋊#108 | C2 | semidirect |
| 2. C2×#19149748 | C2 | semidirect |
| 4. #26012370 | C2 | semidirect |
| 16. #19149687 | C4 | semidirect |
| 17. #19149686 | C4 | semidirect |
| 19. #19149685 | C4 | semidirect |
| 24. #131×C173 | C4 | semidirect |
| 115. C173 | #1816 | semidirect |
| 128. #131 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#108 | 2 |
| C2×#19149748 | 2 |
| #26012482 | 2 |
| #26012370 | 2 |
| #131×D173 | 2 |
| #1816 | 173 |