Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 120. #10623494 | #101 | semidirect |
| 146. C89 | #9794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151994 | 2 |
| #26021096 | 2 |
| #26019007 | 2 |
| #26018937 | 2 |
| #26018925 | 2 |
| M16×#10623494 | 2 |
| C89×#1997 | 2 |
| #9794 | 89 |