Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1146 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 267 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×#19151975 | C2 | semidirect |
| 2. C2×#19151975 | C2 | semidirect |
| 3. C2×#19151971 | C2 | semidirect |
| 4. C2×#19151945 | C2 | semidirect |
| 5. #26019918 | C2 | direct (N × H) |
| 6. C2×#322×C89 | C2 | semidirect |
| 15. #19151975 | C22 | semidirect |
| 16. #19151975 | C22 | semidirect |
| 18. #19151971 | C22 | semidirect |
| 20. #19151945 | C22 | semidirect |
| 24. #322×C89 | C22 | semidirect |
| 85. C2×C8×C89 | D8 | semidirect |
| 120. C8×C89 | C2×D8 | semidirect |
| 137. C2×C89 | #1721 | semidirect |
| 147. C2×#322 | D89 | semidirect |
| 148. C89 | C2×#1721 | semidirect |
| 166. #322 | C2×D89 | semidirect |
| 225. C2×C8 | D712 | semidirect |
| 262. C8 | C2×D712 | semidirect |
| 280. C2 | #26019918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151975 | 2 |
| C2×#19151971 | 2 |
| C2×#19151945 | 2 |
| #26019918 | 2 |
| C2×#322×C89 | 2 |
| C2×#1721 | 89 |