Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012495 | C2 | semidirect |
| 2. C2×#19149744 | C2 | semidirect |
| 3. C42×#10621924 | C2 | semidirect |
| 11. #19149676 | C4 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 16. C4⋊Q8×C173 | C4 | semidirect |
| 22. C4×#10621924 | D4 | semidirect |
| 63. C4×C173 | #104 | semidirect |
| 72. C173 | #1962 | semidirect |
| 80. C4⋊Q8 | #10621924 | semidirect |
| 139. C4 | #19149744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012495 | 2 |
| C2×#19149744 | 2 |
| C42×#10621924 | 2 |
| #26012042 | 2 |
| #1962 | 173 |