Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022089 | C2 | semidirect |
| 3. #26022088 | C2 | semidirect |
| 4. #26018327 | C2 | semidirect |
| 5. #26018226 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C89×#1335 | C2 | semidirect |
| 25. #15667958 | C8 | semidirect |
| 26. #15667956 | C8 | semidirect |
| 27. #15667955 | C8 | semidirect |
| 28. #15667953 | C8 | semidirect |
| 108. #1335 | D89 | semidirect |
| 110. C89 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022131 | 2 |
| #26022089 | 2 |
| #26022088 | 2 |
| #26018327 | 2 |
| #26018226 | 2 |
| C8×#13083549 | 2 |
| C89×#1335 | 2 |
| #12046 | 89 |