Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14583815 | C2 | semidirect |
| 2. C22×#14583814 | C2 | semidirect |
| 4. C2×#19149644 | C2 | semidirect |
| 5. #26011690 | C2 | direct (N × H) |
| 6. C2×#19149608 | C2 | semidirect |
| 7. C2×#19149599 | C2 | semidirect |
| 8. C2×#102×C173 | C2 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 21. #19149644 | C22 | semidirect |
| 25. #19149608 | C22 | semidirect |
| 26. #19149599 | C22 | semidirect |
| 30. #102×C173 | C22 | semidirect |
| 34. C2×Dic346 | D4 | semidirect |
| 72. Dic346 | C2×D4 | semidirect |
| 81. C2×Dic173 | SD16 | semidirect |
| 118. Dic173 | C2×SD16 | semidirect |
| 120. C2×C173 | #460 | semidirect |
| 125. C173 | C2×#460 | semidirect |
| 134. C2×#102 | D173 | semidirect |
| 156. #102 | C2×D173 | semidirect |
| 247. C2 | #26011690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| C22×#14583814 | 2 |
| C2×#19149675 | 2 |
| C2×#19149644 | 2 |
| #26011690 | 2 |
| C2×#19149608 | 2 |
| C2×#19149599 | 2 |
| C2×#102×C173 | 2 |
| C2×#460 | 173 |