Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26031073 | C2 | semidirect |
| 5. #26018773 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1508 | C2 | semidirect |
| 240. #1508 | D89 | semidirect |
| 242. C89 | #10333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031073 | 2 |
| #26023904 | 2 |
| #26023903 | 2 |
| #26020172 | 2 |
| #26018773 | 2 |
| #26018138 | 2 |
| C89×#1508 | 2 |
| #10333 | 89 |