Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26022509 | C2 | semidirect |
| 2. #26022508 | C2 | semidirect |
| 3. #26022507 | C2 | semidirect |
| 4. #26019868 | C2 | semidirect |
| 6. C16×#10623494 | C2 | semidirect |
| 7. C89×#2248 | C2 | semidirect |
| 53. #13083549 | D8 | semidirect |
| 65. C16×C89 | D8 | semidirect |
| 84. #10623494 | SD32 | semidirect |
| 103. #2248 | D89 | semidirect |
| 107. C89 | #12517 | semidirect |
| 165. C16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022509 | 2 |
| #26022508 | 2 |
| #26022507 | 2 |
| #26019868 | 2 |
| #26019866 | 2 |
| C16×#10623494 | 2 |
| C89×#2248 | 2 |
| #12517 | 89 |