Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #26011893 | C2 | semidirect |
| 3. #26011833 | C2 | semidirect |
| 4. #26011827 | C2 | semidirect |
| 5. #26011799 | C2 | semidirect |
| 6. #26011749 | C2 | semidirect |
| 7. C4×Dic692 | C2 | semidirect |
| 8. #26011533 | C2 | semidirect |
| 96. C173 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012181 | 2 |
| #26011893 | 2 |
| #26011833 | 2 |
| #26011827 | 2 |
| #26011799 | 2 |
| #26011749 | 2 |
| C4×Dic692 | 2 |
| #26011533 | 2 |
| #436×C173 | 2 |
| #3352 | 173 |