Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26011443 | C2 | semidirect |
| 3. #97×D173 | C2 | semidirect |
| 4. #26011232 | C2 | semidirect |
| 5. #26011232 | C2 | semidirect |
| 6. #26011231 | C2 | semidirect |
| 7. #329×C173 | C2 | semidirect |
| 99. C173 | #1524 | semidirect |
| 107. #329 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012020 | 2 |
| #26011443 | 2 |
| #97×D173 | 2 |
| #26011232 | 2 |
| #26011231 | 2 |
| #329×C173 | 2 |
| #1524 | 173 |