Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#17984550 | C2 | semidirect |
| 2. C2×D2216 | C2 | semidirect |
| 3. C2×#17984548 | C2 | semidirect |
| 4. #22579876 | C2 | semidirect |
| 5. #22579869 | C2 | semidirect |
| 6. #22579790 | C2 | semidirect |
| 7. C2×SD16×C277 | C2 | semidirect |
| 29. #14555660 | D4 | semidirect |
| 37. C8×C277 | D4 | semidirect |
| 54. C277 | #496 | semidirect |
| 57. C2×SD16 | D277 | semidirect |
| 92. C8 | C22⋊D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984550 | 2 |
| C2×D2216 | 2 |
| C2×#17984548 | 2 |
| #22579876 | 2 |
| #22579869 | 2 |
| #22579790 | 2 |
| C2×SD16×C277 | 2 |
| #496 | 277 |