Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
724 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#19151391 | C2 | semidirect |
| 3. C2×#19151390 | C2 | semidirect |
| 4. C2×#19151390 | C2 | semidirect |
| 5. #26020238 | C2 | semidirect |
| 6. #99×Dic89 | C2 | semidirect |
| 7. C2×#353×C89 | C2 | semidirect |
| 8. C2×#15668008 | C4 | semidirect |
| 17. #19151501 | C4 | semidirect |
| 18. #19151500 | C4 | semidirect |
| 20. C4×#13083553 | C4 | semidirect |
| 65. #15667927 | D4 | semidirect |
| 83. #99×C89 | D4 | semidirect |
| 292. Dic89 | #353 | semidirect |
| 309. C2×#353 | D89 | semidirect |
| 312. C89 | #13223 | semidirect |
| 385. #99 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025196 | 2 |
| C2×#19151391 | 2 |
| C2×#19151390 | 2 |
| #26020238 | 2 |
| #99×Dic89 | 2 |
| C2×#353×C89 | 2 |
| #13223 | 89 |