Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #26011553 | C2 | semidirect |
| 3. #26011550 | C2 | semidirect |
| 4. #26011514 | C2 | semidirect |
| 6. C4×#14583810 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 16. #19149608 | C22 | semidirect |
| 18. #19149590 | C22 | semidirect |
| 19. C4×#13063436 | C22 | semidirect |
| 22. #97×C173 | C22 | semidirect |
| 23. C4×C8×C173 | C22 | semidirect |
| 79. C173 | #2921 | semidirect |
| 87. C4×M16 | D173 | semidirect |
| 101. #97 | C2×D173 | semidirect |
| 103. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149636 | 2 |
| #26011553 | 2 |
| #26011550 | 2 |
| #26011514 | 2 |
| #26011454 | 2 |
| C4×#14583810 | 2 |
| C4×M16×C173 | 2 |
| #2921 | 173 |