Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#19151438 | C2 | semidirect |
| 5. #26018451 | C2 | semidirect |
| 6. #26018434 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 79. C2×D89 | Q64 | semidirect |
| 98. #1416 | D89 | semidirect |
| 99. C89 | #13695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151438 | 2 |
| C2×C32×D89 | 2 |
| #26022344 | 2 |
| #26022340 | 2 |
| #26018451 | 2 |
| #26018434 | 2 |
| C89×#1416 | 2 |
| #13695 | 89 |