Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26012570 | C2 | semidirect |
| 2. #26012490 | C2 | semidirect |
| 3. #26012481 | C2 | semidirect |
| 4. #26012466 | C2 | semidirect |
| 5. #26012374 | C2 | semidirect |
| 6. #26012366 | C2 | semidirect |
| 25. #19149710 | C4 | semidirect |
| 26. #19149707 | C4 | semidirect |
| 28. #19149704 | C4 | semidirect |
| 32. #137×C173 | C4 | semidirect |
| 145. C173 | #1881 | semidirect |
| 158. #137 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012570 | 2 |
| #26012490 | 2 |
| #26012481 | 2 |
| #26012466 | 2 |
| #26012374 | 2 |
| #26012366 | 2 |
| #26012290 | 2 |
| #1881 | 173 |