Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022063 | C2 | semidirect |
| 3. #26018292 | C2 | semidirect |
| 4. #26018289 | C2 | semidirect |
| 5. C89×#1357 | C2 | semidirect |
| 14. #19151419 | C22 | semidirect |
| 18. #364×C89 | C22 | semidirect |
| 131. #1357 | D89 | semidirect |
| 132. C89 | #11992 | semidirect |
| 143. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030703 | 2 |
| #26022063 | 2 |
| #26018292 | 2 |
| #26018289 | 2 |
| C89×#1357 | 2 |
| #11992 | 89 |