Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26012036 | C2 | semidirect |
| 2. #26011895 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011727 | C2 | semidirect |
| 6. #26011725 | C2 | semidirect |
| 7. D8×Dic173 | C2 | semidirect |
| 8. #26011573 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. C2×C8×Dic173 | C2 | semidirect |
| 11. #466×C173 | C2 | semidirect |
| 82. C2×Dic173 | D8 | semidirect |
| 89. #13063436 | #41 | semidirect |
| 101. C8×C173 | #41 | semidirect |
| 127. C173 | #3169 | semidirect |
| 135. #466 | D173 | semidirect |
| 229. C8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| #26011895 | 2 |
| #26011866 | 2 |
| #26011836 | 2 |
| #26011727 | 2 |
| #26011725 | 2 |
| D8×Dic173 | 2 |
| #26011573 | 2 |
| #26011571 | 2 |
| C2×C8×Dic173 | 2 |
| #466×C173 | 2 |
| #3169 | 173 |