Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 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. #26022507 | C2 | semidirect |
| 2. #26022297 | C2 | semidirect |
| 3. #26019617 | C2 | semidirect |
| 4. #26018298 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. D4⋊#13083549 | C2 | semidirect |
| 10. #19151978 | C22 | semidirect |
| 12. C4⋊#13083549 | C22 | semidirect |
| 14. C4×#13083549 | C22 | semidirect |
| 15. #19151351 | C22 | semidirect |
| 112. D4×C89 | SD32 | semidirect |
| 163. C89 | #12320 | semidirect |
| 270. D4 | #15667956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022507 | 2 |
| #26022297 | 2 |
| #26019617 | 2 |
| #26018298 | 2 |
| #26018213 | 2 |
| D4⋊#13083549 | 2 |
| D4×D8×C89 | 2 |
| #12320 | 89 |