Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #26018336 | C2 | semidirect |
| 2. #26018083 | C2 | semidirect |
| 21. C2×D8×C89 | C8 | semidirect |
| 120. C89 | #7110 | semidirect |
| 132. C2×D8 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018336 | 2 |
| #26018083 | 2 |
| C89×#1972 | 2 |
| #7110 | 89 |