Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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. #364×D89 | C2 | semidirect |
| 3. #26018293 | C2 | semidirect |
| 4. #26018292 | C2 | semidirect |
| 5. C89×#1359 | C2 | semidirect |
| 15. #19151419 | C22 | semidirect |
| 18. #364×C89 | C22 | semidirect |
| 140. D89 | #1359 | direct (N × H) |
| 145. #1359 | D89 | direct (N × H) |
| 146. C89 | C2×#1359 | semidirect |
| 159. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #492×D89 | 2 |
| #364×D89 | 2 |
| #26018293 | 2 |
| #26018292 | 2 |
| C89×#1359 | 2 |
| C2×#1359 | 89 |