Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 118. C8×C89 | #101 | semidirect |
| 146. C89 | #9794 | semidirect |
| 259. C8 | #15667930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| #26021240 | 2 |
| #26021095 | 2 |
| #26018938 | 2 |
| #26018925 | 2 |
| C8×#13083558 | 2 |
| C89×#1566 | 2 |
| #9794 | 89 |