Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26011843 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 5. #26011841 | C2 | semidirect |
| 6. #26011840 | C2 | semidirect |
| 9. #487×C173 | C2 | semidirect |
| 108. D173 | #487 | direct (N × H) |
| 109. C173 | C2×#487 | semidirect |
| 117. #487 | D173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #26011843 | 2 |
| #26011842 | 2 |
| #26011841 | 2 |
| #26011840 | 2 |
| #103×D173 | 2 |
| C4×C8×D173 | 2 |
| #487×C173 | 2 |
| C2×#487 | 173 |