Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. #26012549 | C2 | semidirect |
| 2. #26012413 | C2 | semidirect |
| 3. #26012389 | C2 | semidirect |
| 4. #26012380 | C2 | semidirect |
| 49. C173 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012549 | 2 |
| #26012413 | 2 |
| #26012389 | 2 |
| #26012380 | 2 |
| #26011608 | 2 |
| #2171 | 173 |