Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 514 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. C2×#19149653 | C2 | semidirect |
| 2. #26011810 | C2 | semidirect |
| 3. #26011744 | C2 | semidirect |
| 4. #26011627 | C2 | semidirect |
| 5. #407×C173 | C2 | semidirect |
| 6. C22×D692 | C22 | semidirect |
| 8. C2×D1384 | C22 | semidirect |
| 12. #19149653 | C22 | semidirect |
| 13. C2×C4⋊Dic173 | C22 | semidirect |
| 15. #19149611 | C22 | semidirect |
| 16. #19149601 | C22 | semidirect |
| 18. C2×M16×C173 | C22 | semidirect |
| 19. C22⋊C8×C173 | C22 | semidirect |
| 83. C173 | #3192 | semidirect |
| 89. #407 | D173 | semidirect |
| 94. C2×M16 | C2×D173 | semidirect |
| 103. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011810 | 2 |
| #26011744 | 2 |
| #26011627 | 2 |
| #407×C173 | 2 |
| #3192 | 173 |