Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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. #26012440 | C2 | semidirect |
| 3. C4×C4⋊#10621924 | C2 | semidirect |
| 5. #26012427 | C2 | semidirect |
| 6. C42×#10621924 | C2 | semidirect |
| 17. #19149638 | C4 | semidirect |
| 18. #19149637 | C4 | semidirect |
| 19. #19149636 | C4 | semidirect |
| 20. #19149636 | C4 | semidirect |
| 21. #19149635 | C4 | semidirect |
| 26. #117×C173 | C4 | semidirect |
| 108. C173 | #2298 | semidirect |
| 123. #117 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012441 | 2 |
| #26012440 | 2 |
| C4×C4⋊#10621924 | 2 |
| C4×C22⋊#10621924 | 2 |
| #26012427 | 2 |
| C42×#10621924 | 2 |
| #117×D173 | 2 |
| #2298 | 173 |