Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19151645 | C2 | semidirect |
| 3. #26021980 | C2 | semidirect |
| 4. C2×#19151379 | C2 | semidirect |
| 5. #26018367 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C89×#2143 | C2 | semidirect |
| 50. #15667948 | D4 | semidirect |
| 70. #108×C89 | D4 | semidirect |
| 188. #2143 | D89 | semidirect |
| 192. C89 | #12998 | semidirect |
| 251. #108 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029857 | 2 |
| C2×#19151645 | 2 |
| #26021980 | 2 |
| C2×#19151379 | 2 |
| #26018367 | 2 |
| #26018366 | 2 |
| C89×#2143 | 2 |
| #12998 | 89 |