Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1480 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 |
|---|---|---|
| 2. C2×#19151737 | C2 | semidirect |
| 3. #26019220 | C2 | direct (N × H) |
| 4. C2×#19151331 | C2 | semidirect |
| 5. C2×#19151324 | C2 | semidirect |
| 6. C2×#395×C89 | C2 | semidirect |
| 17. #19151737 | C22 | semidirect |
| 20. #19151331 | C22 | semidirect |
| 21. #19151324 | C22 | semidirect |
| 26. #395×C89 | C22 | semidirect |
| 131. C22×C4×C89 | SD16 | semidirect |
| 177. C2×C4×C89 | C2×SD16 | semidirect |
| 219. C2×C89 | #1604 | semidirect |
| 226. C2×#395 | D89 | semidirect |
| 230. C89 | C2×#1604 | semidirect |
| 248. #395 | C2×D89 | semidirect |
| 346. C22×C4 | #13083561 | semidirect |
| 412. C2×C4 | C2×#13083561 | semidirect |
| 443. C2 | #26019220 | 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×#19151737 | 2 |
| #26019220 | 2 |
| C2×#19151331 | 2 |
| C2×#19151324 | 2 |
| C2×#395×C89 | 2 |
| C2×#1604 | 89 |