Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012025 | C2 | semidirect |
| 2. #26011893 | C2 | semidirect |
| 3. #26011875 | C2 | semidirect |
| 4. #26011846 | C2 | semidirect |
| 5. #26011749 | C2 | semidirect |
| 7. #26011737 | C2 | semidirect |
| 8. #26011604 | C2 | semidirect |
| 9. #26011599 | C2 | semidirect |
| 10. #26011593 | C2 | semidirect |
| 11. C4×M16×C173 | C2 | semidirect |
| 109. C173 | #3183 | semidirect |
| 121. C4×M16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011893 | 2 |
| #26011875 | 2 |
| #26011846 | 2 |
| #26011749 | 2 |
| #26011744 | 2 |
| #26011737 | 2 |
| #26011604 | 2 |
| #26011599 | 2 |
| #26011593 | 2 |
| C4×M16×C173 | 2 |
| #3183 | 173 |