Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 10. #19151427 | C4 | direct (N × H) |
| 73. C4×C89 | #368 | semidirect |
| 86. C89 | C4×#368 | semidirect |
| 154. C4 | #19151427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151427 | 2 |
| C2×C4×#13083549 | 2 |
| C4×#15667948 | 2 |
| #26018345 | 2 |
| C4×#108×C89 | 2 |
| C4×#368 | 89 |