Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 720 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. #26022847 | C2 | semidirect |
| 3. #26018768 | C2 | semidirect |
| 4. #26018578 | C2 | semidirect |
| 5. #26018138 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#1507 | C2 | semidirect |
| 12. #19151533 | C4 | semidirect |
| 13. #19151506 | C4 | semidirect |
| 53. #15667919 | D4 | semidirect |
| 68. #95×C89 | D4 | semidirect |
| 226. #1507 | D89 | semidirect |
| 230. C89 | #9413 | semidirect |
| 291. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025184 | 2 |
| #26022847 | 2 |
| #26018768 | 2 |
| #26018578 | 2 |
| #26018138 | 2 |
| #26018137 | 2 |
| C89×#1507 | 2 |
| #9413 | 89 |