Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 169 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. #26018078 | C2 | semidirect |
| 4. #26018077 | C2 | semidirect |
| 5. C89×#1272 | C2 | semidirect |
| 24. C2×Q8×D89 | C8 | semidirect |
| 54. C2×Dic178 | C2×C8 | semidirect |
| 85. C2×Q8×C89 | C2×C8 | semidirect |
| 164. D89 | #1272 | direct (N × H) |
| 169. #1272 | D89 | direct (N × H) |
| 170. C89 | C2×#1272 | semidirect |
| 225. C2×Q8 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #391×D89 | 2 |
| #336×D89 | 2 |
| #26018078 | 2 |
| #26018077 | 2 |
| C89×#1272 | 2 |
| C2×#1272 | 89 |