Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 1. C2×D8×D173 | C2 | semidirect |
| 2. C2×#19149620 | C2 | semidirect |
| 3. #26011724 | C2 | semidirect |
| 4. #26011293 | C2 | semidirect |
| 5. #26011292 | C2 | semidirect |
| 6. #26011270 | C2 | semidirect |
| 7. C2×D16×C173 | C2 | semidirect |
| 16. C2×#14583801 | C22 | semidirect |
| 17. #19149613 | C22 | semidirect |
| 20. C2×D8×C173 | C22 | semidirect |
| 22. C2×C16×C173 | C22 | semidirect |
| 31. D1384 | D4 | semidirect |
| 44. D8×C173 | D4 | semidirect |
| 83. C2×D173 | D16 | semidirect |
| 95. C173 | #2184 | semidirect |
| 99. C2×D16 | D173 | semidirect |
| 110. C2×D8 | C2×D173 | semidirect |
| 116. C2×C16 | C2×D173 | semidirect |
| 134. D8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D173 | 2 |
| C2×#19149620 | 2 |
| #26011724 | 2 |
| #26011293 | 2 |
| #26011292 | 2 |
| #26011270 | 2 |
| C2×D16×C173 | 2 |
| #2184 | 173 |