Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
446 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26018144 | C2 | semidirect |
| 4. #26018118 | C2 | semidirect |
| 174. C89 | #8772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023192 | 2 |
| C4×#15667929 | 2 |
| #26018144 | 2 |
| #26018118 | 2 |
| C89×#1466 | 2 |
| #8772 | 89 |