Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
198 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 62. C16×C89 | Q16 | semidirect |
| 102. C89 | #12459 | semidirect |
| 157. C16 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022534 | 2 |
| #26019656 | 2 |
| #26019646 | 2 |
| #26018326 | 2 |
| #26018309 | 2 |
| #26018306 | 2 |
| Q8×C16×C89 | 2 |
| #12459 | 89 |