Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊#10623494 | C2 | semidirect |
| 3. #26019023 | C2 | semidirect |
| 6. #26018148 | C2 | semidirect |
| 7. C89×#1276 | C2 | semidirect |
| 17. #19151343 | C4 | semidirect |
| 18. #19151341 | C4 | semidirect |
| 162. #1276 | D89 | semidirect |
| 163. C89 | #9578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021080 | 2 |
| C4×C4⋊#10623494 | 2 |
| #26019023 | 2 |
| #26018899 | 2 |
| #26018652 | 2 |
| #26018148 | 2 |
| C89×#1276 | 2 |
| #9578 | 89 |