Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×D692 | C2 | semidirect |
| 2. #26011868 | C2 | semidirect |
| 3. #26011687 | C2 | semidirect |
| 4. #26011686 | C2 | semidirect |
| 5. #26011234 | C2 | semidirect |
| 6. #26011220 | C2 | semidirect |
| 7. D4⋊C8×C173 | C2 | semidirect |
| 14. #19149676 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 23. C4⋊C8×C173 | C22 | semidirect |
| 24. C4×C8×C173 | C22 | semidirect |
| 72. D692 | D8 | semidirect |
| 80. D4×C173 | D8 | semidirect |
| 117. C173 | #1619 | semidirect |
| 125. D4⋊C8 | D173 | semidirect |
| 139. C4⋊C8 | C2×D173 | semidirect |
| 142. C4×C8 | C2×D173 | semidirect |
| 194. D4 | D1384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D692 | 2 |
| #26011868 | 2 |
| #26011687 | 2 |
| #26011686 | 2 |
| #26011234 | 2 |
| #26011220 | 2 |
| D4⋊C8×C173 | 2 |
| #1619 | 173 |