Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
734 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19151322 | C2 | semidirect |
| 2. #26018182 | C2 | semidirect |
| 3. #26018180 | C2 | semidirect |
| 27. C22×D4×C89 | C8 | semidirect |
| 56. C24×C89 | C2×C8 | semidirect |
| 79. C22×C4×C89 | C2×C8 | semidirect |
| 187. C89 | #11426 | semidirect |
| 207. C22×D4 | #10623494 | semidirect |
| 237. C24 | C2×#10623494 | semidirect |
| 260. C22×C4 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151322 | 2 |
| #26018182 | 2 |
| #26018180 | 2 |
| C89×#2308 | 2 |
| #11426 | 89 |