Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4⋊C16×D89 | C2 | semidirect |
| 3. #335×D89 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. #26018298 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 18. C4⋊#13083549 | C22 | semidirect |
| 20. #19151351 | C22 | semidirect |
| 23. C4⋊C16×C89 | C22 | semidirect |
| 24. #335×C89 | C22 | semidirect |
| 160. D89 | #1361 | direct (N × H) |
| 167. #1361 | D89 | direct (N × H) |
| 168. C89 | C2×#1361 | semidirect |
| 182. C4⋊C16 | C2×D89 | semidirect |
| 185. #335 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D89 | 2 |
| C4⋊C16×D89 | 2 |
| #335×D89 | 2 |
| #26018299 | 2 |
| #26018298 | 2 |
| #26018297 | 2 |
| C89×#1361 | 2 |
| C2×#1361 | 89 |