Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26011337 | C2 | semidirect |
| 3. #26011229 | C2 | semidirect |
| 5. #431×C173 | C2 | semidirect |
| 7. #19149671 | C4 | semidirect |
| 8. #19149667 | C4 | semidirect |
| 12. C4×Dic346 | C4 | semidirect |
| 13. C4×D692 | C4 | semidirect |
| 93. C173 | #1500 | semidirect |
| 96. #431 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011337 | 2 |
| #26011229 | 2 |
| #26011226 | 2 |
| #431×C173 | 2 |
| #1500 | 173 |