Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012227 | C2 | semidirect |
| 2. #26012198 | C2 | semidirect |
| 3. #26011844 | C2 | semidirect |
| 4. #26011837 | C2 | semidirect |
| 5. #26011789 | C2 | semidirect |
| 6. #26011787 | C2 | semidirect |
| 7. #26011704 | C2 | semidirect |
| 8. #26011615 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. D8×Dic173 | C2 | semidirect |
| 122. C173 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012227 | 2 |
| #26012198 | 2 |
| #26011844 | 2 |
| #26011837 | 2 |
| #26011789 | 2 |
| #26011787 | 2 |
| #26011704 | 2 |
| #26011615 | 2 |
| C4×#14583814 | 2 |
| D8×Dic173 | 2 |
| #459×C173 | 2 |
| #3361 | 173 |