Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
664 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26028586 | C2 | semidirect |
| 3. #26020318 | C2 | semidirect |
| 4. #26018824 | C2 | semidirect |
| 6. #26018120 | C2 | semidirect |
| 96. C22×Dic89 | SD16 | semidirect |
| 262. C89 | #10323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028586 | 2 |
| #26028578 | 2 |
| #26020318 | 2 |
| #26018824 | 2 |
| #26018820 | 2 |
| #26018120 | 2 |
| C89×#3187 | 2 |
| #10323 | 89 |