Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012060 | C2 | semidirect |
| 2. #26011878 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011857 | C2 | semidirect |
| 5. #26011848 | C2 | semidirect |
| 6. #26011706 | C2 | semidirect |
| 7. #26011686 | C2 | semidirect |
| 8. #26011634 | C2 | semidirect |
| 9. #26011624 | C2 | semidirect |
| 10. #26011552 | C2 | semidirect |
| 11. #540×C173 | C2 | semidirect |
| 14. C2×#14583814 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 24. C4⋊#13063436 | C22 | semidirect |
| 25. #19149602 | C22 | semidirect |
| 28. #19149599 | C22 | semidirect |
| 30. #19149590 | C22 | semidirect |
| 31. C4×#13063436 | C22 | semidirect |
| 32. #127×C173 | C22 | semidirect |
| 33. #125×C173 | C22 | semidirect |
| 37. C4×D4×C173 | C22 | semidirect |
| 128. C173 | #3220 | semidirect |
| 130. #540 | D173 | semidirect |
| 149. #127 | C2×D173 | semidirect |
| 150. #125 | C2×D173 | semidirect |
| 158. C4×D4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| #26011878 | 2 |
| #26011867 | 2 |
| #26011857 | 2 |
| #26011848 | 2 |
| #26011706 | 2 |
| #26011686 | 2 |
| #26011634 | 2 |
| #26011624 | 2 |
| #26011552 | 2 |
| #540×C173 | 2 |
| #3220 | 173 |