Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26033217 | C2 | semidirect |
| 5. #26018305 | C2 | semidirect |
| 6. #26018235 | C2 | semidirect |
| 7. C89×#1334 | C2 | semidirect |
| 88. Q16×C89 | SD16 | semidirect |
| 146. #1334 | D89 | semidirect |
| 147. C89 | #12361 | semidirect |
| 208. Q16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033217 | 2 |
| #26022494 | 2 |
| #26022292 | 2 |
| #26019737 | 2 |
| #26018305 | 2 |
| #26018235 | 2 |
| C89×#1334 | 2 |
| #12361 | 89 |