Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #26012570 | C2 | semidirect |
| 2. #41×#10621924 | C2 | semidirect |
| 3. #26012489 | C2 | semidirect |
| 4. #26012488 | C2 | semidirect |
| 5. D173⋊#104 | C2 | semidirect |
| 6. C2×#19149743 | C2 | semidirect |
| 10. C2×#14583836 | C22 | semidirect |
| 11. D173⋊M16 | C22 | semidirect |
| 14. #19149758 | C22 | semidirect |
| 15. C2×C4×#10621924 | C22 | semidirect |
| 16. #19149744 | C22 | semidirect |
| 17. #19149744 | C22 | semidirect |
| 18. #19149743 | C22 | semidirect |
| 19. #19149743 | C22 | semidirect |
| 20. #19149743 | C22 | semidirect |
| 22. #19149726 | C4 | semidirect |
| 23. #19149726 | C4 | semidirect |
| 25. #19149724 | C4 | semidirect |
| 31. H(5,𝔽2)×C173 | C4 | semidirect |
| 49. #14583826 | C2×C4 | semidirect |
| 56. #14583825 | C2×C4 | semidirect |
| 60. C2×Dic346 | C2×C4 | semidirect |
| 62. Q8×D173 | C2×C4 | semidirect |
| 68. D4×D173 | C2×C4 | semidirect |
| 75. #41×C173 | C2×C4 | semidirect |
| 77. C2×D4×C173 | C2×C4 | semidirect |
| 139. C173 | #2901 | semidirect |
| 153. H(5,𝔽2) | #10621924 | semidirect |
| 189. #41 | C2×#10621924 | semidirect |
| 202. C2×D4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012570 | 2 |
| #41×#10621924 | 2 |
| #26012489 | 2 |
| #26012488 | 2 |
| D173⋊#104 | 2 |
| C2×#19149743 | 2 |
| #26012326 | 2 |
| #2901 | 173 |