Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012119 | C2 | semidirect |
| 3. #26011797 | C2 | semidirect |
| 4. #26011794 | C2 | semidirect |
| 5. #26011780 | C2 | semidirect |
| 6. #26011775 | C2 | semidirect |
| 7. C2×#19149610 | C2 | semidirect |
| 8. #26011519 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 42. #14583826 | Q8 | semidirect |
| 123. C173 | #3084 | semidirect |
| 131. #428 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011972 | 2 |
| #26011797 | 2 |
| #26011794 | 2 |
| #26011780 | 2 |
| #26011775 | 2 |
| C2×#19149610 | 2 |
| #26011519 | 2 |
| #26011493 | 2 |
| #26011485 | 2 |
| #428×C173 | 2 |
| #3084 | 173 |