Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #26011898 | C2 | semidirect |
| 3. #26011891 | C2 | semidirect |
| 4. #26011888 | C2 | semidirect |
| 29. #14583810 | Q8 | semidirect |
| 43. C2×C8×C173 | Q8 | semidirect |
| 75. C173 | #3163 | semidirect |
| 109. C2×C8 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012122 | 2 |
| #26011898 | 2 |
| #26011891 | 2 |
| #26011888 | 2 |
| #26011531 | 2 |
| #26011529 | 2 |
| #26011446 | 2 |
| C2×#106×C173 | 2 |
| #3163 | 173 |