Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
976 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19152229 | C2 | semidirect |
| 3. #26019293 | C2 | semidirect |
| 4. #26019191 | C2 | semidirect |
| 5. #26018771 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 211. C89 | #18326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| #26031058 | 2 |
| #26019293 | 2 |
| #26019191 | 2 |
| #26018771 | 2 |
| #26018582 | 2 |
| C89×#2591 | 2 |
| #18326 | 89 |