Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#19149637 | C2 | semidirect |
| 3. C2×#19149636 | C2 | semidirect |
| 4. #26011394 | C2 | semidirect |
| 5. #26011393 | C2 | semidirect |
| 6. #26011392 | C2 | semidirect |
| 7. #26011391 | C2 | semidirect |
| 8. #26011346 | C2 | semidirect |
| 9. #390×C173 | C2 | semidirect |
| 15. C2×D4×D173 | C4 | semidirect |
| 19. C2×C4⋊Dic173 | C22 | semidirect |
| 20. C2×#14583805 | C22 | semidirect |
| 21. C2×C22⋊Dic173 | C22 | semidirect |
| 24. C2×#14583803 | C22 | semidirect |
| 25. C2×#14583803 | C22 | semidirect |
| 26. C2×C4×Dic173 | C22 | semidirect |
| 27. C2×C4×Dic173 | C22 | semidirect |
| 29. C2×C4⋊C4×C173 | C22 | semidirect |
| 30. C2×C22⋊C4×C173 | C22 | semidirect |
| 31. C2×C42×C173 | C22 | semidirect |
| 96. C4×D173 | C22⋊C4 | semidirect |
| 147. C173 | #2309 | semidirect |
| 156. #390 | D173 | semidirect |
| 170. C2×C4⋊C4 | C2×D173 | semidirect |
| 176. C2×C22⋊C4 | C2×D173 | semidirect |
| 179. C2×C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D173 | 2 |
| C2×#19149637 | 2 |
| C2×#19149636 | 2 |
| #26011394 | 2 |
| #26011393 | 2 |
| #26011392 | 2 |
| #26011391 | 2 |
| #26011346 | 2 |
| #390×C173 | 2 |
| #2309 | 173 |