Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26011613 | C2 | semidirect |
| 3. #26011602 | C2 | semidirect |
| 4. #26011313 | C2 | semidirect |
| 5. #26011305 | C2 | semidirect |
| 6. #26011268 | C2 | semidirect |
| 7. #360×C173 | C2 | semidirect |
| 11. #19149622 | C4 | semidirect |
| 12. #19149620 | C4 | semidirect |
| 31. #14583801 | C2×C4 | semidirect |
| 33. Q16×C173 | C2×C4 | semidirect |
| 35. D8×C173 | C2×C4 | semidirect |
| 68. C173 | AGL(1,ℤ/16) | semidirect |
| 75. #360 | D173 | semidirect |
| 93. Q16 | C4×D173 | semidirect |
| 97. D8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011926 | 2 |
| #26011613 | 2 |
| #26011602 | 2 |
| #26011313 | 2 |
| #26011305 | 2 |
| #26011268 | 2 |
| #360×C173 | 2 |
| AGL(1,ℤ/16) | 173 |