Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
190 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #26018459 | C2 | semidirect |
| 5. #26018458 | C2 | semidirect |
| 6. #26018457 | C2 | semidirect |
| 7. C89×#1426 | C2 | semidirect |
| 12. #19151431 | C4 | semidirect |
| 13. C32×D89 | C4 | semidirect |
| 33. #15667918 | C2×C4 | semidirect |
| 37. C32×C89 | C2×C4 | semidirect |
| 87. D89 | #1426 | direct (N × H) |
| 94. #1426 | D89 | direct (N × H) |
| 95. C89 | C2×#1426 | semidirect |
| 125. C32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D89 | 2 |
| #368×D89 | 2 |
| #367×D89 | 2 |
| #26018459 | 2 |
| #26018458 | 2 |
| #26018457 | 2 |
| C89×#1426 | 2 |
| C2×#1426 | 89 |