Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
464 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 168 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. #26012526 | C2 | semidirect |
| 2. #26012522 | C2 | semidirect |
| 3. D4×#13063443 | C2 | semidirect |
| 4. #26012512 | C2 | semidirect |
| 5. #26012508 | C2 | semidirect |
| 6. #26012461 | C2 | semidirect |
| 7. C2×C22⋊#13063443 | C2 | semidirect |
| 9. C2×#14583835 | C22 | semidirect |
| 10. C22×#13063443 | C22 | semidirect |
| 11. #19149746 | C22 | semidirect |
| 12. C4⋊#13063443 | C22 | semidirect |
| 16. C22⋊#13063443 | C22 | semidirect |
| 17. C22⋊#13063443 | C22 | semidirect |
| 18. #19149734 | C22 | semidirect |
| 19. C4×#13063443 | C22 | semidirect |
| 85. D4×C173 | M16 | semidirect |
| 114. C173 | #2974 | semidirect |
| 184. D4 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012526 | 2 |
| #26012522 | 2 |
| D4×#13063443 | 2 |
| #26012512 | 2 |
| #26012508 | 2 |
| #26012461 | 2 |
| C2×C22⋊#13063443 | 2 |
| C2×D4×Dic173 | 2 |
| #2974 | 173 |