Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26028848 | C2 | semidirect |
| 3. #26021968 | C2 | semidirect |
| 4. C2×#19151381 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C2×#357×C89 | C2 | semidirect |
| 13. #19151865 | C4 | semidirect |
| 51. #15667948 | C2×C4 | semidirect |
| 64. C2×D8×C89 | C2×C4 | semidirect |
| 192. C2×#357 | D89 | semidirect |
| 196. C89 | #12996 | semidirect |
| 228. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151865 | 2 |
| #26028848 | 2 |
| #26021968 | 2 |
| C2×#19151381 | 2 |
| #26018360 | 2 |
| #26018348 | 2 |
| C2×#357×C89 | 2 |
| #12996 | 89 |