Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
258 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 258 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. #26018334 | C2 | semidirect |
| 2. #26018079 | C2 | semidirect |
| 20. C2×Q16×C89 | C8 | semidirect |
| 22. C2×D8×C89 | C8 | semidirect |
| 116. C89 | #7114 | semidirect |
| 127. C2×Q16 | #10623494 | semidirect |
| 129. C2×D8 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018334 | 2 |
| #26018079 | 2 |
| C89×#1974 | 2 |
| #7114 | 89 |