Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26011449 | C2 | semidirect |
| 4. #26011263 | C2 | semidirect |
| 8. C2×#14583810 | C4 | semidirect |
| 10. C22×#13063436 | C4 | semidirect |
| 18. #101×C173 | C4 | semidirect |
| 19. #100×C173 | C4 | semidirect |
| 74. C173 | #1757 | semidirect |
| 90. #101 | Dic173 | semidirect |
| 91. #100 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011465 | 2 |
| #26011449 | 2 |
| #26011263 | 2 |
| #413×C173 | 2 |
| #1757 | 173 |