Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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. #26030812 | C2 | semidirect |
| 3. #26019854 | C2 | semidirect |
| 4. #26019850 | C2 | semidirect |
| 5. #26019845 | C2 | semidirect |
| 6. #26019840 | C2 | semidirect |
| 7. C2×C8×#10623494 | C2 | semidirect |
| 8. C89×#3160 | C2 | semidirect |
| 79. C2×C8×C89 | SD16 | semidirect |
| 109. #10623494 | #135 | semidirect |
| 127. #3160 | D89 | semidirect |
| 134. C89 | #19596 | semidirect |
| 203. C2×C8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030812 | 2 |
| #26030680 | 2 |
| #26019854 | 2 |
| #26019850 | 2 |
| #26019845 | 2 |
| #26019840 | 2 |
| C2×C8×#10623494 | 2 |
| C89×#3160 | 2 |
| #19596 | 89 |