Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022471 | C2 | semidirect |
| 4. #26018241 | C2 | semidirect |
| 5. #26018240 | C2 | semidirect |
| 7. C89×#2239 | C2 | semidirect |
| 149. #2239 | D89 | semidirect |
| 154. C89 | #12302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031144 | 2 |
| #26022471 | 2 |
| #26021804 | 2 |
| #26018241 | 2 |
| #26018240 | 2 |
| #26018189 | 2 |
| C89×#2239 | 2 |
| #12302 | 89 |