Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021244 | C2 | semidirect |
| 3. #26018860 | C2 | semidirect |
| 4. #26018715 | C2 | semidirect |
| 5. #26018669 | C2 | semidirect |
| 6. #26018609 | C2 | semidirect |
| 7. C89×#1557 | C2 | semidirect |
| 251. #1557 | D89 | semidirect |
| 256. C89 | #8486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034790 | 2 |
| #26021244 | 2 |
| #26018860 | 2 |
| #26018715 | 2 |
| #26018669 | 2 |
| #26018609 | 2 |
| C89×#1557 | 2 |
| #8486 | 89 |