Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 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. #26022477 | C2 | semidirect |
| 3. #26019638 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. #26018206 | C2 | semidirect |
| 7. C89×#2224 | C2 | semidirect |
| 17. C4×#13083549 | C22 | semidirect |
| 18. #19151351 | C22 | semidirect |
| 20. #500×C89 | C22 | semidirect |
| 23. C4⋊C16×C89 | C22 | semidirect |
| 83. D8×C89 | SD16 | semidirect |
| 154. #2224 | D89 | semidirect |
| 159. C89 | #12368 | semidirect |
| 162. #500 | C2×D89 | semidirect |
| 171. C4⋊C16 | C2×D89 | semidirect |
| 227. D8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D356 | 2 |
| #26022477 | 2 |
| #26019638 | 2 |
| #26018299 | 2 |
| #26018213 | 2 |
| #26018206 | 2 |
| C89×#2224 | 2 |
| #12368 | 89 |