Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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×#19151435 | C2 | semidirect |
| 2. C2×#19151432 | C2 | semidirect |
| 4. #26018451 | C2 | semidirect |
| 5. #26018433 | C2 | semidirect |
| 6. #26018429 | C2 | semidirect |
| 7. C89×#2216 | C2 | semidirect |
| 28. #15667918 | D4 | semidirect |
| 98. #2216 | D89 | semidirect |
| 103. C89 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151435 | 2 |
| C2×#19151432 | 2 |
| #26022338 | 2 |
| #26018451 | 2 |
| #26018433 | 2 |
| #26018429 | 2 |
| C89×#2216 | 2 |
| #13699 | 89 |