Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 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. C2×#19151423 | C2 | semidirect |
| 3. C2×#19151404 | C2 | semidirect |
| 4. #26021965 | C2 | semidirect |
| 5. C2×#19151383 | C2 | semidirect |
| 6. #26020313 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 51. C2×#13083549 | D4 | semidirect |
| 190. #1387 | D89 | semidirect |
| 191. C89 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029924 | 2 |
| C2×#19151423 | 2 |
| C2×#19151404 | 2 |
| #26021965 | 2 |
| C2×#19151383 | 2 |
| #26020313 | 2 |
| C89×#1387 | 2 |
| #13384 | 89 |