Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
936 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19151407 | C2 | semidirect |
| 3. #26021962 | C2 | semidirect |
| 4. C2×#19151380 | C2 | semidirect |
| 5. C89×#1809 | C2 | semidirect |
| 9. #19152398 | C4 | semidirect |
| 14. C2×#15667952 | C22 | semidirect |
| 20. C2×#107×C89 | C22 | semidirect |
| 21. C2×#106×C89 | C22 | semidirect |
| 98. Dic356 | C22⋊C4 | semidirect |
| 104. D712 | C22⋊C4 | semidirect |
| 211. #1809 | D89 | semidirect |
| 212. C89 | #12739 | semidirect |
| 223. C2×#107 | C2×D89 | semidirect |
| 224. C2×#106 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152398 | 2 |
| C2×#19151407 | 2 |
| #26021962 | 2 |
| C2×#19151380 | 2 |
| C89×#1809 | 2 |
| #12739 | 89 |