Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
190 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26018453 | C2 | semidirect |
| 4. #26018451 | C2 | semidirect |
| 7. C2×#15667918 | C4 | semidirect |
| 70. C89 | #13633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667918 | 2 |
| #26022036 | 2 |
| #26018453 | 2 |
| #26018451 | 2 |
| C89×#2158 | 2 |
| #13633 | 89 |