Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #26012211 | C2 | semidirect |
| 2. #26011894 | C2 | semidirect |
| 3. #26011826 | C2 | semidirect |
| 4. #26011812 | C2 | semidirect |
| 5. #26011773 | C2 | semidirect |
| 6. #26011771 | C2 | semidirect |
| 7. #26011735 | C2 | semidirect |
| 8. C4×#14583814 | C2 | semidirect |
| 9. #26011569 | C2 | semidirect |
| 10. #26011531 | C2 | semidirect |
| 82. #13063436 | #41 | semidirect |
| 122. C173 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012211 | 2 |
| #26011894 | 2 |
| #26011826 | 2 |
| #26011812 | 2 |
| #26011773 | 2 |
| #26011771 | 2 |
| #26011735 | 2 |
| C4×#14583814 | 2 |
| #26011569 | 2 |
| #26011531 | 2 |
| #547×C173 | 2 |
| #3353 | 173 |