Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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. #26012441 | C2 | semidirect |
| 2. #26012433 | C2 | semidirect |
| 4. C4×C22⋊#10621924 | C2 | semidirect |
| 6. C2×C4⋊#10621924 | C22 | semidirect |
| 10. C2×C4×#10621924 | C22 | semidirect |
| 11. (C2×#10621924)⋊C4 | C22 | semidirect |
| 12. (C2×#10621924)⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic173 | C4 | semidirect |
| 17. C2×#14583803 | C4 | semidirect |
| 18. C2×#14583803 | C4 | semidirect |
| 19. C22⋊C4×D173 | C4 | semidirect |
| 21. C2×C22⋊C4×C173 | C4 | semidirect |
| 120. C173 | #2312 | semidirect |
| 139. C2×C22⋊C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012441 | 2 |
| #26012433 | 2 |
| #26012432 | 2 |
| C4×C22⋊#10621924 | 2 |
| C2×C22⋊C4×D173 | 2 |
| #2312 | 173 |