Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #26033386 | C2 | semidirect |
| 2. #26021980 | C2 | semidirect |
| 3. #26021145 | C2 | semidirect |
| 4. #26018332 | C2 | semidirect |
| 5. C89×#3150 | C2 | semidirect |
| 26. C2×Dic356 | D4 | semidirect |
| 28. C2×D712 | D4 | semidirect |
| 36. C2×#13083549 | D4 | semidirect |
| 165. #3150 | D89 | semidirect |
| 169. C89 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26021980 | 2 |
| #26021145 | 2 |
| #26018332 | 2 |
| C89×#3150 | 2 |
| #13340 | 89 |