Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #26011778 | C2 | semidirect |
| 3. #26011235 | C2 | semidirect |
| 4. #26011220 | C2 | semidirect |
| 5. #492×C173 | C2 | semidirect |
| 11. C4⋊#13063436 | C22 | semidirect |
| 14. C4⋊Q8×C173 | C22 | semidirect |
| 16. C4×C8×C173 | C22 | semidirect |
| 38. D692 | SD16 | semidirect |
| 69. C173 | #1629 | semidirect |
| 72. #492 | D173 | semidirect |
| 78. C4⋊Q8 | C2×D173 | semidirect |
| 86. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012126 | 2 |
| #26011778 | 2 |
| #26011235 | 2 |
| #26011220 | 2 |
| #492×C173 | 2 |
| #1629 | 173 |