Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26019015 | C2 | semidirect |
| 4. #26018121 | C2 | semidirect |
| 5. C89×#1568 | C2 | semidirect |
| 138. #1568 | D89 | semidirect |
| 141. C89 | #8620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D356 | 2 |
| #26019015 | 2 |
| #26018592 | 2 |
| #26018121 | 2 |
| C89×#1568 | 2 |
| #8620 | 89 |