Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22579878 | C2 | semidirect |
| 2. #22579870 | C2 | semidirect |
| 3. #22579870 | C2 | semidirect |
| 4. #22579858 | C2 | semidirect |
| 5. #22579858 | C2 | semidirect |
| 6. #22579857 | C2 | semidirect |
| 7. #22579857 | C2 | semidirect |
| 8. #22579856 | C2 | semidirect |
| 9. #22579845 | C2 | semidirect |
| 13. C2×#17984542 | C2 | semidirect |
| 14. C4⋊C4×D277 | C2 | semidirect |
| 15. C22⋊Q8×C277 | C2 | semidirect |
| 54. C22⋊D277 | Q8 | semidirect |
| 101. C277 | #554 | semidirect |
| 111. C22⋊Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579878 | 2 |
| #22579870 | 2 |
| #22579858 | 2 |
| #22579857 | 2 |
| #22579856 | 2 |
| #22579845 | 2 |
| C4×C22⋊D277 | 2 |
| #22579840 | 2 |
| C2×#17984542 | 2 |
| C4⋊C4×D277 | 2 |
| C22⋊Q8×C277 | 2 |
| #554 | 277 |