Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022477 | C2 | semidirect |
| 2. #26022292 | C2 | semidirect |
| 4. #26018310 | C2 | semidirect |
| 5. #26018216 | C2 | semidirect |
| 6. D4⋊#13083549 | C2 | semidirect |
| 7. C89×#3338 | C2 | semidirect |
| 92. D4×C89 | SD32 | semidirect |
| 135. #3338 | D89 | semidirect |
| 142. C89 | #12342 | semidirect |
| 232. D4 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022477 | 2 |
| #26022292 | 2 |
| #26019607 | 2 |
| #26018310 | 2 |
| #26018216 | 2 |
| D4⋊#13083549 | 2 |
| C89×#3338 | 2 |
| #12342 | 89 |