Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1652 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1652 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 |
|---|---|---|
| 1. C2×#19152179 | C2 | semidirect |
| 2. C2×#19151732 | C2 | semidirect |
| 3. #26019186 | C2 | direct (N × H) |
| 4. C2×#19151331 | C2 | semidirect |
| 5. C2×#19151324 | C2 | semidirect |
| 6. C2×#394×C89 | C2 | semidirect |
| 11. #19152179 | C22 | semidirect |
| 17. #19151732 | C22 | semidirect |
| 20. #19151331 | C22 | semidirect |
| 21. #19151324 | C22 | semidirect |
| 27. #394×C89 | C22 | semidirect |
| 136. C22×C4×C89 | D8 | semidirect |
| 195. C2×C4×C89 | C2×D8 | semidirect |
| 246. C2×C89 | #1598 | semidirect |
| 253. C2×#394 | D89 | semidirect |
| 257. C89 | C2×#1598 | semidirect |
| 276. #394 | C2×D89 | semidirect |
| 378. C22×C4 | #13083559 | semidirect |
| 457. C2×C4 | C2×#13083559 | semidirect |
| 497. C2 | #26019186 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| C2×#19151732 | 2 |
| #26019186 | 2 |
| C2×#19151331 | 2 |
| C2×#19151324 | 2 |
| C2×#394×C89 | 2 |
| C2×#1598 | 89 |