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. #26022476 | C2 | semidirect |
| 3. #26022389 | C2 | semidirect |
| 4. #26019642 | C2 | semidirect |
| 5. #26018297 | C2 | semidirect |
| 6. #26018208 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 10. #19152003 | C22 | semidirect |
| 18. C4⋊#13083549 | C22 | semidirect |
| 23. C4×C16×C89 | C22 | semidirect |
| 24. #335×C89 | C22 | semidirect |
| 84. D8×C89 | SD16 | semidirect |
| 157. #1331 | D89 | semidirect |
| 159. C89 | #12368 | semidirect |
| 174. C4×C16 | C2×D89 | semidirect |
| 175. #335 | C2×D89 | semidirect |
| 227. D8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D356 | 2 |
| #26022476 | 2 |
| #26022389 | 2 |
| #26019642 | 2 |
| #26018297 | 2 |
| #26018208 | 2 |
| C89×#1331 | 2 |
| #12368 | 89 |