Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
814 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 251 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. #26022504 | C2 | direct (N × H) |
| 81. C2×C4×C89 | Q32 | semidirect |
| 100. C4×C89 | C2×Q32 | semidirect |
| 105. C2×C89 | #2247 | semidirect |
| 113. C89 | C2×#2247 | semidirect |
| 194. C2×C4 | #15667958 | semidirect |
| 209. C4 | C2×#15667958 | semidirect |
| 212. C2 | #26022504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667958 | 2 |
| C2×#19151978 | 2 |
| #26022504 | 2 |
| C2×C4×#13083549 | 2 |
| C2×#494×C89 | 2 |
| C2×#2247 | 89 |