Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19151933 | C2 | semidirect |
| 4. C2×#19151334 | C2 | semidirect |
| 6. #26018095 | C2 | semidirect |
| 7. C89×#1445 | C2 | semidirect |
| 233. #1445 | D89 | semidirect |
| 235. C89 | #9969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151933 | 2 |
| C2×#19151916 | 2 |
| #26026180 | 2 |
| C2×#19151334 | 2 |
| C2×#19151331 | 2 |
| #26018095 | 2 |
| C89×#1445 | 2 |
| #9969 | 89 |