Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1200 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 203 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. #26019225 | C2 | direct (N × H) |
| 121. C22×C4×C89 | Q16 | semidirect |
| 163. C2×C4×C89 | C2×Q16 | semidirect |
| 198. C2×C89 | #1605 | semidirect |
| 208. C89 | C2×#1605 | semidirect |
| 309. C22×C4 | #13083564 | semidirect |
| 372. C2×C4 | C2×#13083564 | semidirect |
| 399. C2 | #26019225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| C2×#19151754 | 2 |
| #26019225 | 2 |
| C2×#19151334 | 2 |
| C2×#19151324 | 2 |
| C2×#395×C89 | 2 |
| C2×#1605 | 89 |