Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 177. C89 | #10463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030059 | 2 |
| #26020245 | 2 |
| #26018943 | 2 |
| #26018708 | 2 |
| C2×#19151330 | 2 |
| #26018126 | 2 |
| C89×#1567 | 2 |
| #10463 | 89 |