Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #26012258 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. C2×#19149607 | C2 | semidirect |
| 5. C4×#41×C173 | C2 | semidirect |
| 7. #19149726 | C4 | semidirect |
| 8. #19149725 | C4 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 14. #19149607 | C22 | semidirect |
| 15. #19149607 | C22 | semidirect |
| 19. #117×C173 | C22 | semidirect |
| 20. C2×C42×C173 | C22 | semidirect |
| 24. #14583826 | C2×C4 | semidirect |
| 27. C2×Dic346 | C2×C4 | semidirect |
| 29. C2×D692 | C2×C4 | semidirect |
| 83. C173 | #2901 | semidirect |
| 87. C4×#41 | D173 | semidirect |
| 101. #117 | C2×D173 | semidirect |
| 102. C2×C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| #26012258 | 2 |
| #26011509 | 2 |
| C2×#19149607 | 2 |
| C4×#41×C173 | 2 |
| #2901 | 173 |