Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#19149686 | C2 | semidirect |
| 3. #26011495 | C2 | semidirect |
| 4. #26011490 | C2 | semidirect |
| 5. #26011485 | C2 | semidirect |
| 6. C2×#19149599 | C2 | semidirect |
| 7. #520×C173 | C2 | semidirect |
| 9. #19149725 | C4 | semidirect |
| 15. C2×#14583810 | C22 | semidirect |
| 16. C22×#13063436 | C22 | semidirect |
| 17. #19149602 | C22 | semidirect |
| 18. #19149602 | C22 | semidirect |
| 19. #19149599 | C22 | semidirect |
| 20. #19149599 | C22 | semidirect |
| 21. #19149599 | C22 | semidirect |
| 25. #117×C173 | C22 | semidirect |
| 26. C2×C4⋊C4×C173 | C22 | semidirect |
| 30. #14583826 | C2×C4 | semidirect |
| 34. C2×D692 | C2×C4 | semidirect |
| 97. C173 | #2897 | semidirect |
| 101. #520 | D173 | semidirect |
| 118. #117 | C2×D173 | semidirect |
| 119. C2×C4⋊C4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| C2×#19149686 | 2 |
| #26011495 | 2 |
| #26011490 | 2 |
| #26011485 | 2 |
| C2×#19149599 | 2 |
| #520×C173 | 2 |
| #2897 | 173 |