Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019846 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 5. #26018309 | C2 | semidirect |
| 6. #26018301 | C2 | semidirect |
| 90. #10623494 | SD32 | semidirect |
| 115. C89 | #12420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022399 | 2 |
| #26019846 | 2 |
| D8×#10623494 | 2 |
| #26018315 | 2 |
| #26018309 | 2 |
| #26018301 | 2 |
| C89×#2208 | 2 |
| #12420 | 89 |