Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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. C4×#14583810 | C2 | semidirect |
| 3. #26011230 | C2 | semidirect |
| 4. #432×C173 | C2 | semidirect |
| 14. #19149590 | C22 | semidirect |
| 19. #97×C173 | C22 | semidirect |
| 84. C173 | #1527 | semidirect |
| 87. #432 | D173 | semidirect |
| 103. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| C4×#14583810 | 2 |
| #26011230 | 2 |
| #432×C173 | 2 |
| #1527 | 173 |