Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19149603 | C2 | semidirect |
| 3. C2×C4×#13063436 | C2 | semidirect |
| 4. #26011357 | C2 | semidirect |
| 15. #124×C173 | C4 | semidirect |
| 78. C173 | #1958 | semidirect |
| 89. #124 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149603 | 2 |
| C2×#19149600 | 2 |
| C2×C4×#13063436 | 2 |
| #26011357 | 2 |
| C2×#124×C173 | 2 |
| #1958 | 173 |