Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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. #26011619 | C2 | semidirect |
| 3. #26011618 | C2 | semidirect |
| 4. #26011615 | C2 | semidirect |
| 81. C173 | #2985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011619 | 2 |
| #26011618 | 2 |
| #26011615 | 2 |
| #26011549 | 2 |
| #26011544 | 2 |
| #432×C173 | 2 |
| #2985 | 173 |