Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #26011801 | C2 | semidirect |
| 4. #26011800 | C2 | semidirect |
| 5. #26011787 | C2 | semidirect |
| 6. #26011786 | C2 | semidirect |
| 7. #26011773 | C2 | semidirect |
| 11. #475×C173 | C2 | semidirect |
| 47. Q8×D173 | Q8 | semidirect |
| 130. C173 | #3078 | semidirect |
| 139. #475 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4×Q8×D173 | 2 |
| #26011801 | 2 |
| #26011800 | 2 |
| #26011787 | 2 |
| #26011786 | 2 |
| #26011773 | 2 |
| #26011530 | 2 |
| #26011513 | 2 |
| #26011498 | 2 |
| #475×C173 | 2 |
| #3078 | 173 |