Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26031251 | C2 | semidirect |
| 3. #26019567 | C2 | semidirect |
| 4. #26018879 | C2 | semidirect |
| 5. #26018849 | C2 | semidirect |
| 6. C89×#3166 | C2 | semidirect |
| 14. #19151990 | C22 | semidirect |
| 15. #19151960 | C22 | semidirect |
| 20. #19151340 | C22 | semidirect |
| 21. #19151337 | C22 | semidirect |
| 24. #501×C89 | C22 | semidirect |
| 154. #3166 | D89 | semidirect |
| 158. C89 | #19006 | semidirect |
| 168. #501 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152346 | 2 |
| #26031251 | 2 |
| #26019567 | 2 |
| #26018879 | 2 |
| #26018849 | 2 |
| C89×#3166 | 2 |
| #19006 | 89 |