Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012048 | C2 | semidirect |
| 3. #26011851 | C2 | semidirect |
| 4. #26011846 | C2 | semidirect |
| 5. #26011501 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 10. #19149679 | C22 | semidirect |
| 11. #19149671 | C22 | semidirect |
| 19. #19149604 | C22 | semidirect |
| 23. #97×C173 | C22 | semidirect |
| 24. C4×C8×C173 | C22 | semidirect |
| 83. C173 | #3140 | semidirect |
| 91. C4×M16 | D173 | semidirect |
| 107. #97 | C2×D173 | semidirect |
| 108. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×#19149667 | 2 |
| #26011851 | 2 |
| #26011846 | 2 |
| #26011501 | 2 |
| #26011497 | 2 |
| C4×M16×C173 | 2 |
| #3140 | 173 |