Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26018247 | C2 | semidirect |
| 5. #26018246 | C2 | semidirect |
| 6. #26018245 | C2 | semidirect |
| 7. C89×#1342 | C2 | semidirect |
| 197. D89 | #1342 | direct (N × H) |
| 204. #1342 | D89 | direct (N × H) |
| 205. C89 | C2×#1342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #470×D89 | 2 |
| #349×D89 | 2 |
| #338×D89 | 2 |
| #26018247 | 2 |
| #26018246 | 2 |
| #26018245 | 2 |
| C89×#1342 | 2 |
| C2×#1342 | 89 |