Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26031701 | C2 | semidirect |
| 4. #26018271 | C2 | semidirect |
| 5. #26018270 | C2 | semidirect |
| 6. #26018193 | C2 | semidirect |
| 168. C89 | #12165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031701 | 2 |
| #26022181 | 2 |
| #26021505 | 2 |
| #26018271 | 2 |
| #26018270 | 2 |
| #26018193 | 2 |
| C89×#2187 | 2 |
| #12165 | 89 |