Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26022047 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151412 | C2 | semidirect |
| 5. #26020302 | C2 | semidirect |
| 6. #26018364 | C2 | semidirect |
| 7. C89×#2117 | C2 | semidirect |
| 168. #2117 | D89 | semidirect |
| 171. C89 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151868 | 2 |
| #26022047 | 2 |
| C2×#19151412 | 2 |
| #26020302 | 2 |
| #26018364 | 2 |
| C89×#2117 | 2 |
| #13389 | 89 |