Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
698 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#15667953 | C2 | semidirect |
| 2. C2×#19151975 | C2 | semidirect |
| 3. C2×#19151398 | C2 | semidirect |
| 4. #26018330 | C2 | semidirect |
| 5. C89×#1970 | C2 | semidirect |
| 36. C2×#13083549 | D4 | semidirect |
| 41. C2×D8×C89 | D4 | semidirect |
| 109. C2×C4×C89 | D16 | semidirect |
| 156. #1970 | D89 | semidirect |
| 158. C89 | #13325 | semidirect |
| 188. C2×D8 | D356 | semidirect |
| 267. C2×C4 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667953 | 2 |
| C2×#19151975 | 2 |
| C2×#19151398 | 2 |
| #26018330 | 2 |
| C89×#1970 | 2 |
| #13325 | 89 |