Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1050 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26020244 | C2 | semidirect |
| 2. #26018920 | C2 | semidirect |
| 3. #26018681 | C2 | semidirect |
| 4. #26018573 | C2 | semidirect |
| 122. Q8×C89 | #100 | semidirect |
| 188. C89 | #8385 | semidirect |
| 305. Q8 | #15667929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020244 | 2 |
| #26018920 | 2 |
| #26018681 | 2 |
| #26018573 | 2 |
| C2×#550×C89 | 2 |
| #8385 | 89 |