Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D173⋊#131 | C2 | semidirect |
| 2. #26012560 | C2 | semidirect |
| 3. #26012483 | C2 | semidirect |
| 4. #26012482 | C2 | semidirect |
| 5. #26012481 | C2 | semidirect |
| 6. C2×#19149741 | C2 | semidirect |
| 10. D173⋊M16 | C22 | semidirect |
| 11. C2×D173⋊C8 | C22 | semidirect |
| 14. #19149758 | C22 | semidirect |
| 15. C2×C4⋊#10621924 | C22 | semidirect |
| 16. #19149742 | C22 | semidirect |
| 17. #19149742 | C22 | semidirect |
| 18. #19149741 | C22 | semidirect |
| 19. #19149741 | C22 | semidirect |
| 20. #19149741 | C22 | semidirect |
| 22. #19149725 | C4 | semidirect |
| 23. #19149725 | C4 | semidirect |
| 25. #19149724 | C4 | semidirect |
| 31. H(5,𝔽2)×C173 | C4 | semidirect |
| 46. #14583827 | C2×C4 | semidirect |
| 51. #14583826 | C2×C4 | semidirect |
| 54. #14583825 | C2×C4 | semidirect |
| 59. C2×D692 | C2×C4 | semidirect |
| 68. D4×D173 | C2×C4 | semidirect |
| 75. #41×C173 | C2×C4 | semidirect |
| 77. C2×D4×C173 | C2×C4 | semidirect |
| 146. C173 | #2897 | semidirect |
| 160. H(5,𝔽2) | #10621924 | semidirect |
| 193. #41 | C2×#10621924 | semidirect |
| 210. C2×D4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#131 | 2 |
| #26012560 | 2 |
| #26012483 | 2 |
| #26012482 | 2 |
| #26012481 | 2 |
| C2×#19149741 | 2 |
| H(5,𝔽2)×D173 | 2 |
| #2897 | 173 |