Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
782 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19151572 | C2 | semidirect |
| 2. C2×#19151391 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018377 | C2 | semidirect |
| 16. C2×#124×C89 | C4 | semidirect |
| 17. C2×#121×C89 | C4 | semidirect |
| 20. #391×C89 | C4 | semidirect |
| 24. C4×C22⋊C4×C89 | C4 | semidirect |
| 36. #15667927 | D4 | semidirect |
| 271. C89 | #13089 | semidirect |
| 274. C2×#124 | Dic89 | semidirect |
| 275. C2×#121 | Dic89 | semidirect |
| 284. #391 | Dic89 | semidirect |
| 289. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151572 | 2 |
| C2×#19151391 | 2 |
| #26020170 | 2 |
| #26018377 | 2 |
| C89×#2431 | 2 |
| #13089 | 89 |