Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 108. C2×C8×C89 | Q16 | semidirect |
| 177. C89 | #10224 | semidirect |
| 262. C2×C8 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031403 | 2 |
| #26031200 | 2 |
| #26030776 | 2 |
| #26018815 | 2 |
| #26018097 | 2 |
| C89×#1993 | 2 |
| #10224 | 89 |