Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26019000 | C2 | semidirect |
| 3. #26018642 | C2 | semidirect |
| 4. #26018572 | C2 | semidirect |
| 5. C89×#1452 | C2 | semidirect |
| 146. #1452 | D89 | semidirect |
| 147. C89 | #9670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D712 | 2 |
| #26019000 | 2 |
| #26018642 | 2 |
| #26018572 | 2 |
| C89×#1452 | 2 |
| #9670 | 89 |