Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
4830 conjugacy classes of subgroups; only the 1195 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 1195 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 |
|---|---|---|
| 2. #26018523 | C2 | direct (N × H) |
| 8. C23×Q8×C89 | C4 | semidirect |
| 13. C23×Dic89 | Q8 | semidirect |
| 20. C22×Q8×C89 | C2×C4 | semidirect |
| 30. C22×Dic89 | C2×Q8 | semidirect |
| 77. C2×C89 | #1446 | semidirect |
| 85. C89 | C2×#1446 | semidirect |
| 87. C23×Q8 | Dic89 | semidirect |
| 97. C22×Q8 | C2×Dic89 | semidirect |
| 158. C2 | #26018523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667919 | 2 |
| #26018523 | 2 |
| C24×Q8×C89 | 2 |
| C2×#1446 | 89 |