Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19152033 | C2 | semidirect |
| 2. C2×#19151973 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151411 | C2 | semidirect |
| 5. #26021141 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C2×#509×C89 | C2 | semidirect |
| 50. #15667952 | D4 | semidirect |
| 64. C2×Q16×C89 | D4 | semidirect |
| 72. C2×D8×C89 | D4 | semidirect |
| 77. M32×C89 | D4 | semidirect |
| 207. C2×#509 | D89 | semidirect |
| 213. C89 | #13331 | semidirect |
| 245. C2×Q16 | C22⋊D89 | semidirect |
| 262. C2×D8 | C22⋊D89 | semidirect |
| 276. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151973 | 2 |
| C2×#19151412 | 2 |
| C2×#19151411 | 2 |
| #26021141 | 2 |
| #26018333 | 2 |
| C2×#509×C89 | 2 |
| #13331 | 89 |