Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26020248 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 5. C89×#1801 | C2 | semidirect |
| 188. C4×C89 | #355 | semidirect |
| 202. #1801 | D89 | semidirect |
| 204. C89 | #12801 | semidirect |
| 390. C4 | #19151394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668001 | 2 |
| C2×#19151394 | 2 |
| #26020248 | 2 |
| #26018378 | 2 |
| C89×#1801 | 2 |
| #12801 | 89 |