Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26018608 | C2 | semidirect |
| 5. #26018151 | C2 | semidirect |
| 6. #26018097 | C2 | semidirect |
| 7. C2×#330×C89 | C2 | semidirect |
| 197. C2×#330 | D89 | semidirect |
| 201. C89 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031420 | 2 |
| #26029246 | 2 |
| #26018870 | 2 |
| #26018608 | 2 |
| #26018151 | 2 |
| #26018097 | 2 |
| C2×#330×C89 | 2 |
| #9266 | 89 |