Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #26012041 | C2 | semidirect |
| 2. #26011881 | C2 | semidirect |
| 3. #26011850 | C2 | semidirect |
| 4. #26011693 | C2 | semidirect |
| 5. #26011683 | C2 | semidirect |
| 6. #26011636 | C2 | semidirect |
| 7. #26011548 | C2 | semidirect |
| 8. #532×C173 | C2 | semidirect |
| 117. C173 | #3214 | semidirect |
| 120. #532 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011881 | 2 |
| #26011850 | 2 |
| #26011693 | 2 |
| #26011683 | 2 |
| #26011636 | 2 |
| #26011548 | 2 |
| #532×C173 | 2 |
| #3214 | 173 |