Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022609 | C2 | semidirect |
| 3. #26018582 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 16. #395×C89 | C4 | semidirect |
| 17. #394×C89 | C4 | semidirect |
| 138. C2×C4×C89 | #104 | semidirect |
| 181. C89 | #9476 | semidirect |
| 188. #395 | Dic89 | semidirect |
| 189. #394 | Dic89 | semidirect |
| 317. C2×C4 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022609 | 2 |
| #26020196 | 2 |
| #26018582 | 2 |
| #26018104 | 2 |
| C89×#2406 | 2 |
| #9476 | 89 |