Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26011604 | C2 | semidirect |
| 3. #26011315 | C2 | semidirect |
| 4. #26011303 | C2 | semidirect |
| 5. #26011301 | C2 | semidirect |
| 6. #26011269 | C2 | semidirect |
| 7. #444×C173 | C2 | semidirect |
| 10. #19149622 | C4 | semidirect |
| 11. #19149620 | C4 | semidirect |
| 28. #14583801 | C2×C4 | semidirect |
| 30. Q16×C173 | C2×C4 | semidirect |
| 32. D8×C173 | C2×C4 | semidirect |
| 68. C173 | AGL(1,ℤ/16) | semidirect |
| 71. #444 | 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 |
| #26011604 | 2 |
| #26011315 | 2 |
| #26011303 | 2 |
| #26011301 | 2 |
| #26011269 | 2 |
| #444×C173 | 2 |
| AGL(1,ℤ/16) | 173 |