Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26029192 | C2 | semidirect |
| 3. #26018910 | C2 | semidirect |
| 5. #26018149 | C2 | semidirect |
| 6. #26018097 | C2 | semidirect |
| 109. C2×C8×C89 | SD16 | semidirect |
| 196. C89 | #9050 | semidirect |
| 290. C2×C8 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030260 | 2 |
| #26029192 | 2 |
| #26018910 | 2 |
| #26018677 | 2 |
| #26018149 | 2 |
| #26018097 | 2 |
| C89×#1955 | 2 |
| #9050 | 89 |