Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
722 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 722 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 |
|---|---|---|
| 3. #26028287 | C2 | semidirect |
| 5. #26018784 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#1511 | C2 | semidirect |
| 249. #1511 | D89 | semidirect |
| 251. C89 | #9982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029514 | 2 |
| #26029510 | 2 |
| #26028287 | 2 |
| #26020169 | 2 |
| #26018784 | 2 |
| #26018161 | 2 |
| C89×#1511 | 2 |
| #9982 | 89 |