Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22579875 | C2 | semidirect |
| 2. #22579871 | C2 | semidirect |
| 3. #22579869 | C2 | semidirect |
| 4. #22579865 | C2 | semidirect |
| 5. #22579856 | C2 | semidirect |
| 7. C4×D1108 | C2 | semidirect |
| 8. C4×D1108 | C2 | semidirect |
| 9. #22579837 | C2 | semidirect |
| 10. C42×D277 | C2 | semidirect |
| 11. C4×Q8×C277 | C2 | semidirect |
| 74. C277 | #529 | semidirect |
| 82. C4×Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579875 | 2 |
| #22579871 | 2 |
| #22579869 | 2 |
| #22579865 | 2 |
| #22579856 | 2 |
| #22579855 | 2 |
| C4×D1108 | 2 |
| #22579837 | 2 |
| C42×D277 | 2 |
| C4×Q8×C277 | 2 |
| #529 | 277 |