Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149710 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. C2×#19149701 | C2 | semidirect |
| 4. #26012065 | C2 | semidirect |
| 5. #26012058 | C2 | semidirect |
| 6. #26011882 | C2 | semidirect |
| 7. #26011877 | C2 | semidirect |
| 8. #26011872 | C2 | semidirect |
| 9. #26011862 | C2 | semidirect |
| 10. #26011446 | C2 | semidirect |
| 11. C22×SD16×C173 | C2 | semidirect |
| 17. C2×Dic692 | C22 | semidirect |
| 18. C2×#14583816 | C22 | semidirect |
| 19. C2×#14583815 | C22 | semidirect |
| 20. C2×#14583815 | C22 | semidirect |
| 22. C2×#14583813 | C22 | semidirect |
| 23. C2×D1384 | C22 | semidirect |
| 26. #19149677 | C22 | semidirect |
| 28. #19149668 | C22 | semidirect |
| 35. #19149589 | C22 | semidirect |
| 36. C8×Dic173 | C22 | semidirect |
| 64. #14583810 | D4 | semidirect |
| 85. C2×C8×C173 | D4 | semidirect |
| 148. C173 | #3154 | semidirect |
| 153. C22×SD16 | D173 | semidirect |
| 228. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| C2×#19149705 | 2 |
| C2×#19149701 | 2 |
| #26012065 | 2 |
| #26012058 | 2 |
| #26011882 | 2 |
| #26011877 | 2 |
| #26011872 | 2 |
| #26011862 | 2 |
| #26011446 | 2 |
| C22×SD16×C173 | 2 |
| #3154 | 173 |