Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012048 | C2 | semidirect |
| 2. #26011886 | C2 | semidirect |
| 3. #26011850 | C2 | semidirect |
| 4. #26011710 | C2 | semidirect |
| 5. #26011647 | C2 | semidirect |
| 7. #26011548 | C2 | semidirect |
| 9. C2×#14583816 | C22 | semidirect |
| 11. #19149679 | C22 | semidirect |
| 12. #19149679 | C22 | semidirect |
| 17. C4×Dic346 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 20. #19149603 | C22 | semidirect |
| 23. #19149590 | C22 | semidirect |
| 112. C173 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011886 | 2 |
| #26011850 | 2 |
| #26011710 | 2 |
| #26011647 | 2 |
| #26011642 | 2 |
| #26011548 | 2 |
| C2×#124×C173 | 2 |
| #3215 | 173 |