Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018423 | C2 | direct (N × H) |
| 8. C2×#125×C89 | C4 | semidirect |
| 10. #490×C89 | C4 | semidirect |
| 13. C2×#97×C89 | C4 | semidirect |
| 26. #125×C89 | C2×C4 | semidirect |
| 33. #97×C89 | C2×C4 | semidirect |
| 105. C2×C89 | #1412 | semidirect |
| 110. C89 | C2×#1412 | semidirect |
| 112. C2×#125 | Dic89 | semidirect |
| 114. #490 | Dic89 | semidirect |
| 118. C2×#97 | Dic89 | semidirect |
| 130. #125 | C2×Dic89 | semidirect |
| 140. #97 | C2×Dic89 | semidirect |
| 211. C2 | #26018423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26018423 | 2 |
| C2×#490×C89 | 2 |
| C2×#1412 | 89 |