Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 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. C2×#19149758 | C2 | semidirect |
| 2. C2×#19149741 | C2 | semidirect |
| 3. D173⋊(C22⋊C8) | C2 | semidirect |
| 4. #26012364 | C2 | semidirect |
| 17. #19149654 | C4 | semidirect |
| 18. #19149653 | C4 | semidirect |
| 21. #19149650 | C4 | semidirect |
| 24. #121×C173 | C4 | semidirect |
| 30. C4⋊#10621924 | D4 | semidirect |
| 137. C173 | #1875 | semidirect |
| 153. #121 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| C2×#19149741 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012364 | 2 |
| #121×D173 | 2 |
| #1875 | 173 |