Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #26021244 | C2 | semidirect |
| 4. #26018853 | C2 | semidirect |
| 6. #26018123 | C2 | semidirect |
| 7. C89×#1569 | C2 | semidirect |
| 168. #1569 | D89 | semidirect |
| 173. C89 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031444 | 2 |
| #26021244 | 2 |
| #26018972 | 2 |
| #26018853 | 2 |
| #26018843 | 2 |
| #26018123 | 2 |
| C89×#1569 | 2 |
| #10497 | 89 |