Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26021245 | C2 | semidirect |
| 3. #26019020 | C2 | semidirect |
| 5. #26018855 | C2 | semidirect |
| 7. C89×#1291 | C2 | semidirect |
| 172. #1291 | 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 |
| #26021245 | 2 |
| #26019020 | 2 |
| #26018975 | 2 |
| #26018855 | 2 |
| #26018843 | 2 |
| C89×#1291 | 2 |
| #10497 | 89 |