Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 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. #26011447 | C2 | semidirect |
| 3. C4×#14583810 | C2 | semidirect |
| 4. C2×C4×#13063436 | C2 | semidirect |
| 6. #19149686 | C4 | direct (N × H) |
| 18. #14583810 | C2×C4 | semidirect |
| 19. C2×#13063436 | C2×C4 | semidirect |
| 48. C4×C173 | #131 | semidirect |
| 53. C173 | C4×#131 | semidirect |
| 102. C4 | #19149686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011447 | 2 |
| C4×#14583810 | 2 |
| C2×C4×#13063436 | 2 |
| C4×#41×C173 | 2 |
| C4×#131 | 173 |