Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#19149767 | C2 | semidirect |
| 2. #26012535 | C2 | direct (N × H) |
| 3. C2×#19149750 | C2 | semidirect |
| 4. C2×#19149744 | C2 | semidirect |
| 5. C2×C8×#10621924 | C2 | semidirect |
| 8. #19149767 | C22 | semidirect |
| 14. #19149750 | C22 | semidirect |
| 15. #19149744 | C22 | semidirect |
| 16. C8×#10621924 | C22 | semidirect |
| 18. #19149702 | C4 | semidirect |
| 20. C2×#14583813 | C4 | semidirect |
| 21. C2×D1384 | C4 | semidirect |
| 23. C2×Q16×C173 | C4 | semidirect |
| 44. #14583813 | C2×C4 | semidirect |
| 45. D1384 | C2×C4 | semidirect |
| 50. Q16×C173 | C2×C4 | semidirect |
| 88. C2×C173 | #443 | semidirect |
| 93. C173 | C2×#443 | semidirect |
| 104. C2×Q16 | #10621924 | semidirect |
| 128. Q16 | C2×#10621924 | semidirect |
| 185. C2 | #26012535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| #26012535 | 2 |
| C2×#19149750 | 2 |
| C2×#19149744 | 2 |
| C2×C8×#10621924 | 2 |
| C2×#19149702 | 2 |
| C2×#443 | 173 |