Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14583811 | C2 | semidirect |
| 2. C23×#13063436 | C2 | semidirect |
| 3. C2×#19149653 | C2 | semidirect |
| 4. #26011725 | C2 | direct (N × H) |
| 5. C2×#19149612 | C2 | semidirect |
| 6. C2×#19149600 | C2 | semidirect |
| 7. C2×#19149599 | C2 | semidirect |
| 8. C2×#121×C173 | C2 | semidirect |
| 12. C2×#14583811 | C22 | semidirect |
| 16. C22×#13063436 | C22 | semidirect |
| 18. #19149653 | C22 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149600 | C22 | semidirect |
| 23. #19149599 | C22 | semidirect |
| 28. #121×C173 | C22 | semidirect |
| 42. C2×#13063436 | D4 | semidirect |
| 77. #13063436 | C2×D4 | semidirect |
| 84. C23×C173 | D8 | semidirect |
| 111. C22×C173 | C2×D8 | semidirect |
| 126. C2×C173 | #466 | semidirect |
| 131. C173 | C2×#466 | semidirect |
| 136. C2×#121 | D173 | semidirect |
| 155. #121 | C2×D173 | semidirect |
| 208. C23 | #14583811 | semidirect |
| 247. C22 | C2×#14583811 | semidirect |
| 259. C2 | #26011725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C23×#13063436 | 2 |
| C2×#19149653 | 2 |
| #26011725 | 2 |
| C2×#19149612 | 2 |
| C2×#19149600 | 2 |
| C2×#19149599 | 2 |
| C2×#121×C173 | 2 |
| C2×#466 | 173 |