Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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. D173⋊(C22⋊C8) | C2 | semidirect |
| 2. C4×C22⋊#10621924 | C2 | semidirect |
| 3. #26012345 | C2 | semidirect |
| 4. #26012342 | C2 | semidirect |
| 14. #19149655 | C4 | semidirect |
| 16. #19149650 | C4 | semidirect |
| 21. #19149638 | C4 | semidirect |
| 22. C2×#41×C173 | C4 | semidirect |
| 112. C173 | #1501 | semidirect |
| 119. C2×#41 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C22⋊C8) | 2 |
| C4×C22⋊#10621924 | 2 |
| #26012345 | 2 |
| #26012342 | 2 |
| #26011998 | 2 |
| #1501 | 173 |