Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
562 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#19151916 | C2 | semidirect |
| 3. C2×#19151911 | C2 | semidirect |
| 4. #26018613 | C2 | semidirect |
| 5. #26018613 | C2 | semidirect |
| 6. #26018139 | C2 | semidirect |
| 7. C89×#1821 | C2 | semidirect |
| 206. #1821 | D89 | semidirect |
| 210. C89 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031052 | 2 |
| C2×#19151916 | 2 |
| C2×#19151911 | 2 |
| #26018613 | 2 |
| #26018139 | 2 |
| C89×#1821 | 2 |
| #9992 | 89 |