Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #26011841 | C2 | semidirect |
| 4. #26011825 | C2 | semidirect |
| 5. #26011787 | C2 | semidirect |
| 6. #26011729 | C2 | semidirect |
| 7. #26011645 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 10. #103×D173 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 81. D692 | Q16 | semidirect |
| 122. C173 | #3299 | semidirect |
| 130. #462 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| #26012156 | 2 |
| #26011841 | 2 |
| #26011825 | 2 |
| #26011787 | 2 |
| #26011729 | 2 |
| #26011645 | 2 |
| C4×#14583816 | 2 |
| #26011556 | 2 |
| #103×D173 | 2 |
| #462×C173 | 2 |
| #3299 | 173 |