Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 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. #26022481 | C2 | semidirect |
| 2. #26022302 | C2 | semidirect |
| 4. #26018310 | C2 | semidirect |
| 5. #26018216 | C2 | semidirect |
| 90. D4×C89 | Q32 | semidirect |
| 135. C89 | #12346 | semidirect |
| 220. D4 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022481 | 2 |
| #26022302 | 2 |
| #26019617 | 2 |
| #26018310 | 2 |
| #26018216 | 2 |
| D4⋊#13083549 | 2 |
| C89×#3338 | 2 |
| #12346 | 89 |