Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
890 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19151753 | C2 | semidirect |
| 4. #26020188 | C2 | semidirect |
| 6. #26018131 | C2 | semidirect |
| 7. C2×#328×C89 | C2 | semidirect |
| 87. C23×D89 | Q16 | semidirect |
| 268. C2×#328 | D89 | semidirect |
| 271. C89 | #9924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151753 | 2 |
| #26026059 | 2 |
| C2×#19151511 | 2 |
| #26020188 | 2 |
| C2×#19151321 | 2 |
| #26018131 | 2 |
| C2×#328×C89 | 2 |
| #9924 | 89 |