Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022288 | C2 | semidirect |
| 2. #26019867 | C2 | semidirect |
| 3. C8×D712 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. C89×#1370 | C2 | semidirect |
| 47. D712 | D8 | semidirect |
| 77. C8×C89 | D16 | semidirect |
| 103. #1370 | D89 | semidirect |
| 105. C89 | #12424 | semidirect |
| 178. C8 | D1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022288 | 2 |
| #26019867 | 2 |
| C8×D712 | 2 |
| #26018299 | 2 |
| C89×#1370 | 2 |
| #12424 | 89 |