Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26011834 | C2 | semidirect |
| 3. #26011828 | C2 | semidirect |
| 4. #26011795 | C2 | semidirect |
| 5. #26011750 | C2 | semidirect |
| 6. C4×Dic692 | C2 | semidirect |
| 8. #26011530 | C2 | semidirect |
| 9. #499×C173 | C2 | semidirect |
| 96. C173 | #3352 | semidirect |
| 99. #499 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012179 | 2 |
| #26011834 | 2 |
| #26011828 | 2 |
| #26011795 | 2 |
| #26011750 | 2 |
| C4×Dic692 | 2 |
| #26011570 | 2 |
| #26011530 | 2 |
| #499×C173 | 2 |
| #3352 | 173 |