Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26012354 | C2 | semidirect |
| 4. #26012353 | C2 | semidirect |
| 64. C173 | #1574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012510 | 2 |
| #26012495 | 2 |
| #26012354 | 2 |
| #26012353 | 2 |
| #26011543 | 2 |
| #1574 | 173 |