Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1044 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023904 | C2 | semidirect |
| 3. #26020172 | C2 | semidirect |
| 4. #26018772 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#3193 | C2 | semidirect |
| 55. #15667919 | D4 | semidirect |
| 56. C22×Q8×C89 | D4 | semidirect |
| 61. C2×M16×C89 | D4 | semidirect |
| 72. C2×C4⋊C4×C89 | D4 | semidirect |
| 248. #3193 | D89 | semidirect |
| 255. C89 | #10329 | semidirect |
| 280. C22×Q8 | C22⋊D89 | semidirect |
| 294. C2×M16 | C22⋊D89 | semidirect |
| 308. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023904 | 2 |
| #26023890 | 2 |
| #26020172 | 2 |
| #26018772 | 2 |
| #26018768 | 2 |
| #26018137 | 2 |
| C89×#3193 | 2 |
| #10329 | 89 |