Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 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. #26012041 | C2 | semidirect |
| 2. #26012025 | C2 | semidirect |
| 3. #26011900 | C2 | semidirect |
| 4. #26011880 | C2 | semidirect |
| 5. #26011856 | C2 | semidirect |
| 6. #26011851 | C2 | semidirect |
| 7. #26011744 | C2 | semidirect |
| 8. #26011737 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. C4×D1384 | C2 | semidirect |
| 11. C4×M16×C173 | C2 | semidirect |
| 110. C8×C173 | #41 | semidirect |
| 137. C173 | #3171 | semidirect |
| 149. C4×M16 | D173 | semidirect |
| 248. C8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26012025 | 2 |
| #26011900 | 2 |
| #26011880 | 2 |
| #26011856 | 2 |
| #26011851 | 2 |
| #26011744 | 2 |
| #26011737 | 2 |
| C4×#14583815 | 2 |
| C4×D1384 | 2 |
| C4×M16×C173 | 2 |
| #3171 | 173 |