Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012112 | C2 | semidirect |
| 2. #26011889 | C2 | semidirect |
| 3. #26011875 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011749 | C2 | semidirect |
| 7. #26011720 | C2 | semidirect |
| 8. #26011604 | C2 | semidirect |
| 9. #26011599 | C2 | semidirect |
| 10. C4×#14583815 | C2 | semidirect |
| 11. #405×C173 | C2 | semidirect |
| 109. C173 | #3173 | semidirect |
| 121. #405 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012112 | 2 |
| #26011889 | 2 |
| #26011875 | 2 |
| #26011851 | 2 |
| #26011749 | 2 |
| #26011744 | 2 |
| #26011720 | 2 |
| #26011604 | 2 |
| #26011599 | 2 |
| C4×#14583815 | 2 |
| #405×C173 | 2 |
| #3173 | 173 |