Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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×#19151974 | C2 | semidirect |
| 3. #26019866 | C2 | direct (N × H) |
| 4. C2×C8×#10623494 | C2 | semidirect |
| 5. C2×#493×C89 | C2 | semidirect |
| 10. #19151975 | C22 | semidirect |
| 12. #19151974 | C22 | semidirect |
| 14. C8×#10623494 | C22 | semidirect |
| 18. #493×C89 | C22 | semidirect |
| 52. C2×#10623494 | D8 | semidirect |
| 64. C2×C8×C89 | D8 | semidirect |
| 90. C8×C89 | C2×D8 | semidirect |
| 91. #10623494 | C2×D8 | semidirect |
| 107. C2×C89 | #1712 | semidirect |
| 113. C2×#493 | D89 | semidirect |
| 116. C89 | C2×#1712 | semidirect |
| 127. #493 | C2×D89 | semidirect |
| 175. C2×C8 | #13083559 | semidirect |
| 202. C8 | C2×#13083559 | semidirect |
| 218. C2 | #26019866 | 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×#19151974 | 2 |
| #26019866 | 2 |
| C2×C8×#10623494 | 2 |
| C2×#493×C89 | 2 |
| C2×#1712 | 89 |