Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #26011826 | C2 | semidirect |
| 4. #26011798 | C2 | semidirect |
| 5. #26011713 | C2 | semidirect |
| 6. #26011647 | C2 | semidirect |
| 8. #26011596 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 11. C2×C4×Q8×C173 | C2 | semidirect |
| 131. C173 | #3117 | semidirect |
| 134. C2×C4×Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011826 | 2 |
| #26011809 | 2 |
| #26011798 | 2 |
| #26011713 | 2 |
| #26011647 | 2 |
| #26011630 | 2 |
| #26011596 | 2 |
| #26011589 | 2 |
| #26011548 | 2 |
| C2×C4×Q8×C173 | 2 |
| #3117 | 173 |