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. #26011798 | C2 | semidirect |
| 3. #26011795 | C2 | semidirect |
| 6. #26011701 | C2 | semidirect |
| 7. #26011698 | C2 | semidirect |
| 94. C173 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012103 | 2 |
| #26011798 | 2 |
| #26011795 | 2 |
| #26011747 | 2 |
| #26011730 | 2 |
| #26011701 | 2 |
| #26011698 | 2 |
| #26011518 | 2 |
| #541×C173 | 2 |
| #3261 | 173 |