Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26011449 | C2 | semidirect |
| 5. #26011447 | C2 | semidirect |
| 6. #26011262 | C2 | semidirect |
| 7. #344×C173 | C2 | semidirect |
| 14. C2×#14583809 | C4 | semidirect |
| 16. C2×C8×D173 | C4 | semidirect |
| 18. #19149597 | C4 | semidirect |
| 19. #19149595 | C4 | semidirect |
| 106. C173 | #1757 | semidirect |
| 114. #344 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149687 | 2 |
| #26011473 | 2 |
| #26011464 | 2 |
| #26011449 | 2 |
| #26011447 | 2 |
| #26011262 | 2 |
| #344×C173 | 2 |
| #1757 | 173 |