Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149673 | C2 | semidirect |
| 3. #26011386 | C2 | semidirect |
| 4. #26011385 | C2 | semidirect |
| 5. #26011381 | C2 | semidirect |
| 6. C42×Dic173 | C2 | semidirect |
| 7. C2×#126×C173 | C2 | semidirect |
| 39. C42×C173 | D4 | semidirect |
| 74. Dic173 | #126 | semidirect |
| 80. C173 | #2860 | semidirect |
| 83. C2×#126 | D173 | semidirect |
| 120. C42 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149673 | 2 |
| #26011391 | 2 |
| #26011386 | 2 |
| #26011385 | 2 |
| #26011381 | 2 |
| C42×Dic173 | 2 |
| C2×#126×C173 | 2 |
| #2860 | 173 |