Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#19149749 | C2 | semidirect |
| 2. #26012501 | C2 | semidirect |
| 4. #26012374 | C2 | semidirect |
| 16. #19149687 | C4 | semidirect |
| 17. #19149686 | C4 | semidirect |
| 19. #19149685 | C4 | semidirect |
| 24. #131×C173 | C4 | semidirect |
| 111. C173 | #1814 | semidirect |
| 124. #131 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149749 | 2 |
| #26012501 | 2 |
| #26012488 | 2 |
| #26012374 | 2 |
| #131×D173 | 2 |
| #1814 | 173 |