Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3774 conjugacy classes of subgroups; only the 1579 normal subgroups are shown.
This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1579 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. #26028650 | C2 | direct (N × H) |
| 22. C2×C42×C89 | Q8 | semidirect |
| 37. C42×C89 | C2×Q8 | semidirect |
| 42. C2×C4×C89 | C4⋊Q8 | semidirect |
| 54. C4×C89 | C2×C4⋊Q8 | semidirect |
| 57. C2×C89 | #2868 | semidirect |
| 64. C89 | C2×#2868 | semidirect |
| 81. C2×C42 | Dic178 | semidirect |
| 97. C42 | C2×Dic178 | semidirect |
| 105. C2×C4 | #15668012 | semidirect |
| 115. C4 | C2×#15668012 | semidirect |
| 116. C2 | #26028650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668012 | 2 |
| #26028650 | 2 |
| C2×#19151468 | 2 |
| C2×C43×C89 | 2 |
| C2×#2868 | 89 |