Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 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. #26021228 | C2 | semidirect |
| 3. #26021081 | C2 | semidirect |
| 4. #26021079 | C2 | semidirect |
| 5. #26018989 | C2 | semidirect |
| 6. #26018985 | C2 | semidirect |
| 7. C89×#1560 | C2 | semidirect |
| 8. #19152342 | C4 | semidirect |
| 247. #1560 | D89 | semidirect |
| 248. C89 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034650 | 2 |
| #26021228 | 2 |
| #26021081 | 2 |
| #26021079 | 2 |
| #26018989 | 2 |
| #26018985 | 2 |
| C89×#1560 | 2 |
| #8532 | 89 |