Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 3. #26011698 | C2 | semidirect |
| 4. #26011237 | C2 | semidirect |
| 5. #26011223 | C2 | semidirect |
| 7. #500×C173 | C2 | semidirect |
| 55. D692 | Q16 | semidirect |
| 92. C173 | #1649 | semidirect |
| 95. #500 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012156 | 2 |
| #26011768 | 2 |
| #26011698 | 2 |
| #26011237 | 2 |
| #26011223 | 2 |
| #26011220 | 2 |
| #500×C173 | 2 |
| #1649 | 173 |