Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1002 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 187 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×#19152229 | C2 | semidirect |
| 3. #26019259 | C2 | semidirect |
| 4. #26019191 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 6. C2×#19151324 | C2 | semidirect |
| 120. C22×C4×C89 | SD16 | semidirect |
| 222. C89 | #18294 | semidirect |
| 321. C22×C4 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| #26031009 | 2 |
| #26019259 | 2 |
| #26019191 | 2 |
| #26018823 | 2 |
| C2×#19151324 | 2 |
| C89×#2618 | 2 |
| #18294 | 89 |