Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×D4×Dic173 | C2 | semidirect |
| 3. C2×#19149641 | C2 | semidirect |
| 4. #26011571 | C2 | direct (N × H) |
| 5. C2×#19149612 | C2 | semidirect |
| 6. C2×#19149601 | C2 | semidirect |
| 7. C2×C8×Dic173 | C2 | semidirect |
| 8. C2×#102×C173 | C2 | semidirect |
| 12. C2×#14583811 | C4 | semidirect |
| 16. D4×Dic173 | C22 | semidirect |
| 18. #19149641 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149601 | C22 | semidirect |
| 25. C8×Dic173 | C22 | semidirect |
| 29. #102×C173 | C22 | semidirect |
| 33. C2×D692 | C2×C4 | semidirect |
| 42. #14583811 | C2×C4 | semidirect |
| 43. C2×#13063436 | C2×C4 | semidirect |
| 54. C2×D4×C173 | C2×C4 | semidirect |
| 68. D692 | C22×C4 | semidirect |
| 73. C2×Dic173 | D8 | semidirect |
| 77. #13063436 | C22×C4 | semidirect |
| 85. D4×C173 | C22×C4 | semidirect |
| 111. Dic173 | C2×D8 | semidirect |
| 113. C2×C173 | C4×D8 | semidirect |
| 118. C173 | C2×C4×D8 | semidirect |
| 126. C2×#102 | D173 | semidirect |
| 147. #102 | C2×D173 | semidirect |
| 157. C2×D4 | C4×D173 | semidirect |
| 195. D4 | C2×C4×D173 | semidirect |
| 233. C2 | #26011571 | 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 |
| C2×D4×Dic173 | 2 |
| C2×#19149641 | 2 |
| #26011571 | 2 |
| C2×#19149612 | 2 |
| C2×#19149601 | 2 |
| C2×C8×Dic173 | 2 |
| C2×#102×C173 | 2 |
| C2×C4×D8 | 173 |