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. #26011867 | C2 | semidirect |
| 3. #26011683 | C2 | semidirect |
| 4. #26011234 | C2 | semidirect |
| 5. D4⋊#13063436 | C2 | semidirect |
| 6. #26011218 | C2 | semidirect |
| 7. #459×C173 | C2 | semidirect |
| 17. C4⋊#13063436 | C22 | semidirect |
| 19. C4×#13063436 | C22 | semidirect |
| 21. #127×C173 | C22 | semidirect |
| 23. C4⋊C8×C173 | C22 | semidirect |
| 66. D692 | D8 | semidirect |
| 81. D4×C173 | D8 | semidirect |
| 117. C173 | #1619 | semidirect |
| 122. #459 | D173 | semidirect |
| 132. #127 | C2×D173 | semidirect |
| 139. C4⋊C8 | C2×D173 | semidirect |
| 194. D4 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D692 | 2 |
| #26011867 | 2 |
| #26011683 | 2 |
| #26011234 | 2 |
| D4⋊#13063436 | 2 |
| #26011218 | 2 |
| #459×C173 | 2 |
| #1619 | 173 |