Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. #26011313 | C2 | semidirect |
| 4. #26011308 | C2 | semidirect |
| 5. #26011306 | C2 | semidirect |
| 7. #365×C173 | C2 | semidirect |
| 61. C173 | #2239 | semidirect |
| 66. #365 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011750 | 2 |
| #26011538 | 2 |
| #26011313 | 2 |
| #26011308 | 2 |
| #26011306 | 2 |
| #26011272 | 2 |
| #365×C173 | 2 |
| #2239 | 173 |