Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 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. #26012156 | C2 | semidirect |
| 3. #26011820 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 5. #26011723 | C2 | semidirect |
| 6. #26011693 | C2 | semidirect |
| 7. #26011631 | C2 | semidirect |
| 8. C4×#14583815 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #103×D173 | C2 | semidirect |
| 11. #487×C173 | C2 | semidirect |
| 81. Dic346 | #41 | semidirect |
| 85. D692 | SD16 | semidirect |
| 128. C173 | #3298 | semidirect |
| 132. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012156 | 2 |
| #26012144 | 2 |
| #26011820 | 2 |
| #26011773 | 2 |
| #26011723 | 2 |
| #26011693 | 2 |
| #26011631 | 2 |
| C4×#14583815 | 2 |
| C8×D692 | 2 |
| #103×D173 | 2 |
| #487×C173 | 2 |
| #3298 | 173 |