Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26011573 | C2 | semidirect |
| 3. #26011291 | C2 | semidirect |
| 4. C16×Dic173 | C2 | semidirect |
| 5. #366×C173 | C2 | semidirect |
| 8. D2768 | C4 | semidirect |
| 17. D1384 | C2×C4 | semidirect |
| 24. C16×C173 | C2×C4 | semidirect |
| 44. Dic173 | D16 | semidirect |
| 49. C173 | C4×D16 | semidirect |
| 53. #366 | D173 | semidirect |
| 74. C16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2768 | 2 |
| #26011573 | 2 |
| #26011291 | 2 |
| C16×Dic173 | 2 |
| #366×C173 | 2 |
| C4×D16 | 173 |