Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26011799 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 65. C173 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012103 | 2 |
| #26011799 | 2 |
| #26011749 | 2 |
| #26011732 | 2 |
| #26011702 | 2 |
| #424×C173 | 2 |
| #3261 | 173 |