Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19149687 | C2 | semidirect |
| 3. #26011561 | C2 | semidirect |
| 4. #26011459 | C2 | semidirect |
| 5. C2×#19149590 | C2 | semidirect |
| 6. #423×C173 | C2 | semidirect |
| 32. C2×#13063436 | D4 | semidirect |
| 79. C173 | #2932 | semidirect |
| 84. #423 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149687 | 2 |
| #26012041 | 2 |
| #26011561 | 2 |
| #26011459 | 2 |
| C2×#19149590 | 2 |
| #423×C173 | 2 |
| #2932 | 173 |