Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
994 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 994 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×#19151996 | C2 | semidirect |
| 2. C2×#19151994 | C2 | semidirect |
| 4. #26019838 | C2 | direct (N × H) |
| 5. C2×C8×#10623494 | C2 | semidirect |
| 10. #19151996 | C22 | semidirect |
| 12. #19151994 | C22 | semidirect |
| 18. C8×#10623494 | C22 | semidirect |
| 60. C2×#10623494 | SD16 | semidirect |
| 80. C2×C8×C89 | SD16 | semidirect |
| 109. C8×C89 | C2×SD16 | semidirect |
| 110. #10623494 | C2×SD16 | semidirect |
| 125. C2×C89 | #1705 | semidirect |
| 134. C89 | C2×#1705 | semidirect |
| 204. C2×C8 | #13083562 | semidirect |
| 238. C8 | C2×#13083562 | semidirect |
| 252. C2 | #26019838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| C2×#19151994 | 2 |
| C2×#19151970 | 2 |
| #26019838 | 2 |
| C2×C8×#10623494 | 2 |
| C2×#492×C89 | 2 |
| C2×#1705 | 89 |