Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022509 | C2 | semidirect |
| 3. #26019614 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. #26018206 | C2 | semidirect |
| 7. C89×#2208 | C2 | semidirect |
| 17. C4×#13083549 | C22 | semidirect |
| 18. #19151351 | C22 | semidirect |
| 21. #494×C89 | C22 | semidirect |
| 23. C4⋊C16×C89 | C22 | semidirect |
| 122. D356 | SD32 | semidirect |
| 158. #2208 | D89 | semidirect |
| 163. C89 | #12320 | semidirect |
| 168. #494 | C2×D89 | semidirect |
| 176. C4⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D356 | 2 |
| #26022509 | 2 |
| #26019614 | 2 |
| #26018299 | 2 |
| #26018213 | 2 |
| #26018206 | 2 |
| C89×#2208 | 2 |
| #12320 | 89 |