Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 69. C2×C8×C89 | Q16 | semidirect |
| 126. C89 | #10037 | semidirect |
| 186. C2×C8 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030287 | 2 |
| #26021192 | 2 |
| #26018655 | 2 |
| #26018083 | 2 |
| C89×#3162 | 2 |
| #10037 | 89 |