Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19149667 | C2 | semidirect |
| 2. #26011873 | C2 | semidirect |
| 3. #26011848 | C2 | semidirect |
| 4. #26011713 | C2 | semidirect |
| 5. #26011706 | C2 | semidirect |
| 6. #26011646 | C2 | semidirect |
| 7. #26011641 | C2 | semidirect |
| 8. #26011629 | C2 | semidirect |
| 10. #26011544 | C2 | semidirect |
| 11. #529×C173 | C2 | semidirect |
| 14. C2×#14583816 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 24. C4⋊#13063436 | C22 | semidirect |
| 25. #19149602 | C22 | semidirect |
| 26. #19149602 | C22 | semidirect |
| 31. C4×#13063436 | C22 | semidirect |
| 33. #125×C173 | C22 | semidirect |
| 34. #124×C173 | C22 | semidirect |
| 38. C4×Q8×C173 | C22 | semidirect |
| 40. C4×D4×C173 | C22 | semidirect |
| 143. C173 | #3211 | semidirect |
| 145. #529 | D173 | semidirect |
| 163. #125 | C2×D173 | semidirect |
| 168. #124 | C2×D173 | semidirect |
| 172. C4×Q8 | C2×D173 | semidirect |
| 174. C4×D4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| #26011873 | 2 |
| #26011848 | 2 |
| #26011713 | 2 |
| #26011706 | 2 |
| #26011646 | 2 |
| #26011641 | 2 |
| #26011629 | 2 |
| #26011624 | 2 |
| #26011544 | 2 |
| #529×C173 | 2 |
| #3211 | 173 |