Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 476 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. #26022169 | C2 | semidirect |
| 3. #26021259 | C2 | semidirect |
| 4. #26018262 | C2 | semidirect |
| 5. #26018261 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#2185 | C2 | semidirect |
| 20. C22⋊#13083549 | C22 | semidirect |
| 21. #19151361 | C22 | semidirect |
| 22. C22×Q16×C89 | C22 | semidirect |
| 26. C22⋊C16×C89 | C22 | semidirect |
| 129. C22×D89 | SD32 | semidirect |
| 202. #2185 | D89 | semidirect |
| 207. C89 | #12105 | semidirect |
| 208. C22×Q16 | C2×D89 | semidirect |
| 225. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030999 | 2 |
| #26022169 | 2 |
| #26021259 | 2 |
| #26018262 | 2 |
| #26018261 | 2 |
| #26018175 | 2 |
| C89×#2185 | 2 |
| #12105 | 89 |