Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 5. #19149758 | C4 | semidirect |
| 12. C2×C4⋊Dic173 | C4 | semidirect |
| 14. C2×C4×Dic173 | C4 | semidirect |
| 15. C2×C4⋊C4×C173 | C4 | semidirect |
| 86. C173 | #1740 | semidirect |
| 98. C2×C4⋊C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| #26012369 | 2 |
| C2×#19149637 | 2 |
| #1740 | 173 |