Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
320 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#19149605 | C2 | semidirect |
| 3. #26011337 | C2 | semidirect |
| 4. #423×C173 | C2 | semidirect |
| 6. #19149679 | C4 | semidirect |
| 7. #19149676 | C4 | semidirect |
| 8. #19149667 | C4 | semidirect |
| 28. C4×Dic173 | D4 | semidirect |
| 71. C173 | #1963 | semidirect |
| 74. #423 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149605 | 2 |
| #26011337 | 2 |
| #423×C173 | 2 |
| #1963 | 173 |