Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
696 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26020339 | C2 | semidirect |
| 4. #26018132 | C2 | semidirect |
| 9. #19151523 | C4 | semidirect |
| 171. C89 | #9028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151523 | 2 |
| #26022850 | 2 |
| #26020339 | 2 |
| #26018132 | 2 |
| C2×#323×C89 | 2 |
| #9028 | 89 |