Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19151398 | C2 | semidirect |
| 3. C2×#19151373 | C2 | semidirect |
| 4. #26021116 | C2 | semidirect |
| 5. C2×#367×C89 | C2 | semidirect |
| 9. C2×D1424 | C4 | semidirect |
| 72. C16×C89 | C22⋊C4 | semidirect |
| 120. C2×#367 | D89 | semidirect |
| 124. C89 | #13239 | semidirect |
| 191. C16 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151398 | 2 |
| C2×#19151373 | 2 |
| #26021116 | 2 |
| C2×#367×C89 | 2 |
| #13239 | 89 |