Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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. #26011888 | C2 | semidirect |
| 3. #26011315 | C2 | semidirect |
| 4. #26011311 | C2 | semidirect |
| 7. #365×C173 | C2 | semidirect |
| 21. Dic692 | Q8 | semidirect |
| 23. D1384 | Q8 | semidirect |
| 60. C173 | #2230 | semidirect |
| 65. #365 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011888 | 2 |
| #26011607 | 2 |
| #26011315 | 2 |
| #26011311 | 2 |
| #26011302 | 2 |
| #26011300 | 2 |
| #365×C173 | 2 |
| #2230 | 173 |