Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3678 conjugacy classes of subgroups; only the 1219 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1219 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×#19151466 | C2 | semidirect |
| 3. C2×#19151465 | C2 | semidirect |
| 4. #383×D89 | C2 | direct (N × H) |
| 6. C2×#383×C89 | C2 | semidirect |
| 10. C2×C42×D89 | C4 | semidirect |
| 12. #19151466 | C22 | semidirect |
| 13. #19151465 | C22 | semidirect |
| 18. #383×C89 | C22 | semidirect |
| 28. C2×C4×Dic89 | C2×C4 | semidirect |
| 30. C42×D89 | C2×C4 | semidirect |
| 35. C2×C42×C89 | C2×C4 | semidirect |
| 51. C4×Dic89 | C22×C4 | semidirect |
| 58. C42×C89 | C22×C4 | semidirect |
| 82. C2×D89 | #383 | direct (N × H) |
| 90. C2×C89 | C2×#383 | semidirect |
| 93. D89 | C2×#383 | direct (N × H) |
| 98. C2×#383 | D89 | direct (N × H) |
| 100. C89 | C22×#383 | semidirect |
| 109. #383 | C2×D89 | direct (N × H) |
| 127. C2×C42 | C4×D89 | semidirect |
| 152. C42 | C2×C4×D89 | semidirect |
| 184. C2 | #383×D89 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D89 | 2 |
| C2×#19151466 | 2 |
| C2×#19151465 | 2 |
| #383×D89 | 2 |
| C2×#95×D89 | 2 |
| C2×#383×C89 | 2 |
| C22×#383 | 89 |