Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #26022475 | C2 | semidirect |
| 2. #26022389 | C2 | semidirect |
| 3. #26019641 | C2 | semidirect |
| 4. #26018298 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. D4⋊#13083549 | C2 | semidirect |
| 8. #19152003 | C22 | semidirect |
| 11. C4⋊#13083549 | C22 | semidirect |
| 14. C4×#13083549 | C22 | semidirect |
| 15. #19151351 | C22 | semidirect |
| 80. D8×C89 | SD16 | semidirect |
| 159. C89 | #12368 | semidirect |
| 227. D8 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022475 | 2 |
| #26022389 | 2 |
| #26019641 | 2 |
| #26018298 | 2 |
| #26018213 | 2 |
| D4⋊#13083549 | 2 |
| D4×D8×C89 | 2 |
| #12368 | 89 |