Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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×#19151438 | C2 | semidirect |
| 3. C2×#19151435 | C2 | semidirect |
| 4. #26018432 | C2 | semidirect |
| 5. #26018429 | C2 | semidirect |
| 6. C22⋊#15667918 | C2 | semidirect |
| 7. C89×#2216 | C2 | semidirect |
| 114. #2216 | D89 | semidirect |
| 118. C89 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C2×#19151438 | 2 |
| C2×#19151435 | 2 |
| #26018432 | 2 |
| #26018429 | 2 |
| C22⋊#15667918 | 2 |
| C89×#2216 | 2 |
| #13666 | 89 |