Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021999 | C2 | semidirect |
| 3. C2×#19151406 | C2 | semidirect |
| 4. C2×#19151381 | C2 | semidirect |
| 5. #26020299 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C2×#368×C89 | C2 | semidirect |
| 176. C2×#368 | D89 | semidirect |
| 182. C89 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029973 | 2 |
| #26021999 | 2 |
| C2×#19151406 | 2 |
| C2×#19151381 | 2 |
| #26020299 | 2 |
| #26018355 | 2 |
| C2×#368×C89 | 2 |
| #13392 | 89 |