Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26011805 | C2 | semidirect |
| 3. #26011727 | C2 | semidirect |
| 4. #26011627 | C2 | semidirect |
| 5. C2×C22⋊C8×C173 | C2 | semidirect |
| 6. C22×D692 | C22 | semidirect |
| 8. C2×D1384 | C22 | semidirect |
| 12. #19149653 | C22 | semidirect |
| 13. C2×C4⋊Dic173 | C22 | semidirect |
| 15. #19149613 | C22 | semidirect |
| 16. #19149601 | C22 | semidirect |
| 18. C22×C8×C173 | C22 | semidirect |
| 19. C22⋊C8×C173 | C22 | semidirect |
| 53. C23×C173 | D8 | semidirect |
| 86. C173 | #3186 | semidirect |
| 92. C2×C22⋊C8 | D173 | semidirect |
| 97. C22×C8 | C2×D173 | semidirect |
| 106. C22⋊C8 | C2×D173 | semidirect |
| 134. C23 | D1384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011805 | 2 |
| #26011727 | 2 |
| #26011627 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #3186 | 173 |