Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
968 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 968 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151737 | C2 | semidirect |
| 3. C2×#19151509 | C2 | semidirect |
| 4. C2×#19151333 | C2 | semidirect |
| 5. C2×#19151321 | C2 | semidirect |
| 6. #26018130 | C2 | semidirect |
| 7. C89×#1787 | C2 | semidirect |
| 60. C22⋊#10623494 | D4 | semidirect |
| 64. #15667919 | D4 | semidirect |
| 71. C22×Q8×C89 | D4 | semidirect |
| 90. C23×D89 | SD16 | semidirect |
| 289. #1787 | D89 | semidirect |
| 293. C89 | #9916 | semidirect |
| 324. C22×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151737 | 2 |
| #26025989 | 2 |
| C2×#19151509 | 2 |
| C2×#19151333 | 2 |
| C2×#19151321 | 2 |
| #26018130 | 2 |
| C89×#1787 | 2 |
| #9916 | 89 |