Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #26012206 | C2 | semidirect |
| 2. #26011837 | C2 | semidirect |
| 3. #26011812 | C2 | semidirect |
| 4. #26011786 | C2 | semidirect |
| 5. #26011725 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011636 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. D4×#13063436 | C2 | semidirect |
| 10. #26011487 | C2 | semidirect |
| 11. #550×C173 | C2 | semidirect |
| 132. C173 | #3305 | semidirect |
| 135. #550 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012206 | 2 |
| #26011837 | 2 |
| #26011812 | 2 |
| #26011786 | 2 |
| #26011725 | 2 |
| #26011683 | 2 |
| #26011636 | 2 |
| C4×#14583813 | 2 |
| D4×#13063436 | 2 |
| #26011487 | 2 |
| #550×C173 | 2 |
| #3305 | 173 |