Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 15. #19149612 | C4 | semidirect |
| 16. #19149611 | C4 | semidirect |
| 17. #106×C173 | C4 | semidirect |
| 66. C173 | #1945 | semidirect |
| 81. #106 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149749 | 2 |
| #26012498 | 2 |
| C2×C8×#10621924 | 2 |
| #26012361 | 2 |
| #26011526 | 2 |
| #1945 | 173 |