Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012028 | C2 | semidirect |
| 2. #26011892 | C2 | semidirect |
| 3. #26011876 | C2 | semidirect |
| 4. #26011847 | C2 | semidirect |
| 5. #26011729 | C2 | semidirect |
| 7. #26011723 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. C4×D1384 | C2 | semidirect |
| 10. C4×C8×D173 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 118. C173 | #3168 | semidirect |
| 127. C4×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012028 | 2 |
| #26011892 | 2 |
| #26011876 | 2 |
| #26011847 | 2 |
| #26011729 | 2 |
| #26011728 | 2 |
| #26011723 | 2 |
| C4×#14583813 | 2 |
| C4×D1384 | 2 |
| C4×C8×D173 | 2 |
| C4×Q16×C173 | 2 |
| #3168 | 173 |