Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012214 | C2 | semidirect |
| 3. #26011837 | C2 | semidirect |
| 4. #26011814 | C2 | semidirect |
| 5. #26011777 | C2 | semidirect |
| 6. #26011717 | C2 | semidirect |
| 7. #26011650 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #26011484 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 127. C173 | #3304 | semidirect |
| 135. #460 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26012161 | 2 |
| #26011837 | 2 |
| #26011814 | 2 |
| #26011777 | 2 |
| #26011717 | 2 |
| #26011650 | 2 |
| C4×#14583816 | 2 |
| #26011556 | 2 |
| #26011484 | 2 |
| #460×C173 | 2 |
| #3304 | 173 |