Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012095 | C2 | semidirect |
| 2. #26011893 | C2 | semidirect |
| 3. #26011855 | C2 | semidirect |
| 4. #26011741 | C2 | semidirect |
| 5. #26011724 | C2 | semidirect |
| 6. #26011603 | C2 | semidirect |
| 7. D8×Dic173 | C2 | semidirect |
| 8. #26011445 | C2 | semidirect |
| 9. #493×C173 | C2 | semidirect |
| 84. C173 | #3176 | semidirect |
| 88. #493 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012095 | 2 |
| #26011893 | 2 |
| #26011855 | 2 |
| #26011741 | 2 |
| #26011724 | 2 |
| #26011603 | 2 |
| D8×Dic173 | 2 |
| #26011445 | 2 |
| #493×C173 | 2 |
| #3176 | 173 |