Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26030378 | C2 | semidirect |
| 5. #26018698 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1515 | C2 | semidirect |
| 200. #1515 | D89 | semidirect |
| 203. C89 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030641 | 2 |
| #26030378 | 2 |
| #26026115 | 2 |
| #26018875 | 2 |
| #26018698 | 2 |
| #26018116 | 2 |
| C89×#1515 | 2 |
| #10024 | 89 |