Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26012048 | C2 | semidirect |
| 3. #26011900 | C2 | semidirect |
| 4. #26011885 | C2 | semidirect |
| 5. #26011860 | C2 | semidirect |
| 6. #26011851 | C2 | semidirect |
| 7. #26011749 | C2 | semidirect |
| 9. C4×Dic692 | C2 | semidirect |
| 10. C4×#14583815 | C2 | semidirect |
| 11. C4×M16×C173 | C2 | semidirect |
| 129. C173 | #3172 | semidirect |
| 141. C4×M16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26012025 | 2 |
| #26011900 | 2 |
| #26011885 | 2 |
| #26011860 | 2 |
| #26011851 | 2 |
| #26011749 | 2 |
| #26011737 | 2 |
| C4×Dic692 | 2 |
| C4×#14583815 | 2 |
| C4×M16×C173 | 2 |
| #3172 | 173 |