Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #26011446 | C2 | semidirect |
| 5. #26011263 | C2 | semidirect |
| 6. #26011261 | C2 | semidirect |
| 7. #405×C173 | C2 | semidirect |
| 15. C2×#14583809 | C4 | semidirect |
| 16. C2×C8×D173 | C4 | semidirect |
| 18. #19149597 | C4 | semidirect |
| 19. #19149595 | C4 | semidirect |
| 106. C173 | #1757 | semidirect |
| 112. #405 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149685 | 2 |
| #26011473 | 2 |
| #26011464 | 2 |
| #26011446 | 2 |
| #26011263 | 2 |
| #26011261 | 2 |
| #405×C173 | 2 |
| #1757 | 173 |