Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26018937 | C2 | semidirect |
| 5. #26018143 | C2 | semidirect |
| 6. #26018141 | C2 | semidirect |
| 7. C89×#1549 | C2 | semidirect |
| 178. #1549 | D89 | semidirect |
| 181. C89 | #9435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030709 | 2 |
| #26029318 | 2 |
| #26018985 | 2 |
| #26018937 | 2 |
| #26018143 | 2 |
| #26018141 | 2 |
| C89×#1549 | 2 |
| #9435 | 89 |