Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
754 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #26021240 | C2 | semidirect |
| 3. #26021095 | C2 | semidirect |
| 4. #26018844 | C2 | semidirect |
| 5. #26018689 | C2 | semidirect |
| 6. #26018689 | C2 | semidirect |
| 7. C89×#1560 | C2 | semidirect |
| 238. #1560 | D89 | semidirect |
| 242. C89 | #8470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034159 | 2 |
| #26021240 | 2 |
| #26021095 | 2 |
| #26018844 | 2 |
| #26018689 | 2 |
| C89×#1560 | 2 |
| #8470 | 89 |