Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 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. #26022163 | C2 | semidirect |
| 2. #26021563 | C2 | semidirect |
| 3. #26018261 | C2 | semidirect |
| 4. #26018192 | C2 | semidirect |
| 5. C89×#3245 | C2 | semidirect |
| 108. C2×C4×C89 | D16 | semidirect |
| 150. #3245 | D89 | semidirect |
| 155. C89 | #12158 | semidirect |
| 265. C2×C4 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022163 | 2 |
| #26021563 | 2 |
| #26018261 | 2 |
| #26018192 | 2 |
| C89×#3245 | 2 |
| #12158 | 89 |