Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26031974 | C2 | semidirect |
| 2. #26022507 | C2 | semidirect |
| 3. #26022284 | C2 | semidirect |
| 4. #26018300 | C2 | semidirect |
| 5. #26018212 | C2 | semidirect |
| 6. D4⋊#13083549 | C2 | semidirect |
| 7. C89×#1667 | C2 | semidirect |
| 68. D712 | D8 | semidirect |
| 154. #1667 | D89 | semidirect |
| 158. C89 | #12319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031974 | 2 |
| #26022507 | 2 |
| #26022284 | 2 |
| #26018300 | 2 |
| #26018212 | 2 |
| D4⋊#13083549 | 2 |
| C89×#1667 | 2 |
| #12319 | 89 |