Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#19149767 | C2 | semidirect |
| 2. #26012525 | C2 | semidirect |
| 3. #26012519 | C2 | semidirect |
| 4. #26012495 | C2 | semidirect |
| 5. #26012466 | C2 | semidirect |
| 6. C4×D173⋊C8 | C2 | semidirect |
| 29. D173⋊C8 | D4 | semidirect |
| 75. C4×C173 | #131 | semidirect |
| 83. C173 | #2931 | semidirect |
| 162. C4 | #19149767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| #26012525 | 2 |
| #26012519 | 2 |
| #26012495 | 2 |
| #26012466 | 2 |
| C4×D173⋊C8 | 2 |
| #26012042 | 2 |
| #2931 | 173 |