Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26012257 | C2 | semidirect |
| 3. #26011507 | C2 | semidirect |
| 4. #26011488 | C2 | semidirect |
| 5. #26011457 | C2 | semidirect |
| 6. #26011263 | C2 | semidirect |
| 7. #341×C173 | C2 | semidirect |
| 11. #19149712 | C4 | semidirect |
| 13. #19149707 | C4 | semidirect |
| 118. C173 | #1881 | semidirect |
| 126. #341 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| #26012257 | 2 |
| #26011507 | 2 |
| #26011488 | 2 |
| #26011457 | 2 |
| #26011263 | 2 |
| #341×C173 | 2 |
| #1881 | 173 |