Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #26011883 | C2 | semidirect |
| 3. #26011865 | C2 | semidirect |
| 4. #26011857 | C2 | semidirect |
| 5. #26011848 | C2 | semidirect |
| 6. #26011713 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011651 | C2 | semidirect |
| 9. #26011641 | C2 | semidirect |
| 10. #26011552 | C2 | semidirect |
| 11. #541×C173 | C2 | semidirect |
| 14. C2×#14583816 | C22 | semidirect |
| 17. C2×#14583813 | 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. C4⋊Q8×C173 | C22 | semidirect |
| 35. #125×C173 | C22 | semidirect |
| 37. C4×Q8×C173 | C22 | semidirect |
| 122. C173 | #3222 | semidirect |
| 124. #541 | D173 | semidirect |
| 141. C4⋊Q8 | C2×D173 | semidirect |
| 146. #125 | C2×D173 | semidirect |
| 152. C4×Q8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| #26011883 | 2 |
| #26011865 | 2 |
| #26011857 | 2 |
| #26011848 | 2 |
| #26011713 | 2 |
| #26011691 | 2 |
| #26011651 | 2 |
| #26011641 | 2 |
| #26011552 | 2 |
| #541×C173 | 2 |
| #3222 | 173 |