Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #22579913 | C2 | semidirect |
| 3. C2×#17984552 | C2 | semidirect |
| 4. #22579886 | C2 | semidirect |
| 5. #22579798 | C2 | semidirect |
| 6. #22579796 | C2 | semidirect |
| 7. #108×C277 | C2 | semidirect |
| 51. C277 | #471 | semidirect |
| 57. #108 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579913 | 2 |
| #22579908 | 2 |
| C2×#17984552 | 2 |
| #22579886 | 2 |
| #22579798 | 2 |
| #22579796 | 2 |
| #108×C277 | 2 |
| #471 | 277 |