Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #26012506 | C2 | semidirect |
| 4. M16×#10621924 | C2 | semidirect |
| 5. #26012374 | C2 | semidirect |
| 6. #26012363 | C2 | semidirect |
| 23. #19149597 | C4 | semidirect |
| 24. #19149597 | C4 | semidirect |
| 25. #19149596 | C4 | semidirect |
| 26. #100×C173 | C4 | semidirect |
| 105. C173 | #1932 | semidirect |
| 130. #100 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012506 | 2 |
| #26012489 | 2 |
| C2×#19149743 | 2 |
| M16×#10621924 | 2 |
| #26012374 | 2 |
| #26012363 | 2 |
| #26011472 | 2 |
| #1932 | 173 |